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155-699: Development economics involves the creation of theories and methods that aid in the determination of policies and practices and can be implemented at either the domestic or international level. This may involve restructuring market incentives or using mathematical methods such as intertemporal optimization for project analysis, or it may involve a mixture of quantitative and qualitative methods. Common topics include growth theory, poverty and inequality, human capital , and institutions. Unlike in many other fields of economics, approaches in development economics may incorporate social and political factors to devise particular plans. Also unlike many other fields of economics, there

310-655: A log cabin in Kentucky and was raised on the frontier , mainly in Indiana . He was self-educated and became a lawyer, Whig Party leader, Illinois state legislator , and U.S. representative from Illinois . In 1849, he returned to his successful law practice in Springfield, Illinois . In 1854, angered by the Kansas–Nebraska Act , which opened the territories to slavery, he re-entered politics. He soon became

465-480: A raconteur , but lacked the requisite formal education, powerful friends, and money, and lost the election. Lincoln finished eighth out of 13 candidates (the top four were elected), though he received 277 of the 300 votes cast in the New Salem precinct. Lincoln served as New Salem's postmaster and later as county surveyor, but continued his voracious reading and decided to become a lawyer. Rather than studying in

620-455: A 'first-order condition' or a set of first-order conditions. Optima of equality-constrained problems can be found by the Lagrange multiplier method. The optima of problems with equality and/or inequality constraints can be found using the ' Karush–Kuhn–Tucker conditions '. While the first derivative test identifies points that might be extrema, this test does not distinguish a point that is

775-422: A candidate solution satisfies the first-order conditions, then the satisfaction of the second-order conditions as well is sufficient to establish at least local optimality. The envelope theorem describes how the value of an optimal solution changes when an underlying parameter changes. The process of computing this change is called comparative statics . The maximum theorem of Claude Berge (1963) describes

930-450: A civil war were more sensitive to the quality of the legal system than similar firms that had never been exposed to conflict. Per capita Gross Domestic Product (GDP per head) , real income , median income and disposable income are used by many developmental economists as an approximation of general national well-being. However, these measures are criticized as not measuring economic growth well enough, especially in countries where there

1085-509: A compromise; the measure would allow the electorate of each territory to decide the status of slavery. The legislation alarmed many Northerners, who sought to prevent the spread of slavery that could result, but Douglas's Kansas–Nebraska Act narrowly passed Congress in May 1854. Lincoln did not comment on the act until months later in his " Peoria Speech " of October 1854. Lincoln then declared his opposition to slavery, which he repeated en route to

1240-482: A concept dating back to the account of the Tower of Babel : that linguistic unity may allow for higher levels of development. While pointing out obvious oversimplifications and the subjectivity of definitions and data collection, Pool suggested that we had yet to see a robust economy emerge from a nation with a high degree of linguistic diversity. In his research Pool used the "size of the largest native-language community as

1395-518: A condition now thought to be clinical depression . Later in life, Mary struggled with the stresses of losing her husband and sons, and in 1875 Robert committed her to an asylum. During 1831 and 1832, Lincoln worked at a general store in New Salem, Illinois . In 1832, he declared his candidacy for the Illinois House of Representatives , but interrupted his campaign to serve as a captain in

1550-490: A disciple of Henry Clay". Their party favored economic modernization in banking, tariffs to fund internal improvements including railroads, and urbanization. In 1843, Lincoln sought the Whig nomination for Illinois's 7th district seat in the U.S. House of Representatives ; he was defeated by John J. Hardin , though he prevailed with the party in limiting Hardin to one term. Lincoln not only pulled off his strategy of gaining

1705-594: A federal court for his freedom. His petition was denied in Dred Scott v. Sandford (1857). In his opinion, Supreme Court Chief Justice Roger B. Taney wrote that black people were not citizens and derived no rights from the Constitution, and that the Missouri Compromise was unconstitutional for infringing upon slave owners' "property" rights. While many Democrats hoped that Dred Scott would end

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1860-594: A formidable trial combatant during cross-examinations and closing arguments. He partnered several years with Stephen T. Logan , and in 1844, began his practice with William Herndon , "a studious young man". On January 27, 1838, Abraham Lincoln, then 28 years old, delivered his first major speech at the Lyceum in Springfield, Illinois , after the murder of newspaper editor Elijah Parish Lovejoy in Alton. Lincoln warned that no trans-Atlantic military giant could ever crush

2015-737: A group largely loyal to Chase, Lincoln shrewdly made no reference to either of these Republican rivals for the nomination." In response to an inquiry about his ambitions, Lincoln said, "The taste is in my mouth a little". On May 9–10, 1860, the Illinois Republican State Convention was held in Decatur . Lincoln's followers organized a campaign team led by David Davis , Norman Judd , Leonard Swett , and Jesse DuBois, and Lincoln received his first endorsement. Exploiting his embellished frontier legend (clearing land and splitting fence rails), Lincoln's supporters adopted

2170-438: A household including her father, nine-year-old Abraham, and Nancy's 19-year-old orphan cousin, Dennis Hanks. Ten years later, on January 20, 1828, Sarah died while giving birth to a stillborn son, devastating Lincoln. On December 2, 1819, Thomas married Sarah Bush Johnston , a widow from Elizabethtown, Kentucky, with three children of her own. Abraham became close to his stepmother and called her "Mother". Dennis Hanks said he

2325-692: A killing of American soldiers by Mexican cavalry patrol in disputed territory, and Polk insisted that Mexican soldiers had "invaded our territory and shed the blood of our fellow-citizens on our own soil". Lincoln demanded that Polk show Congress the exact spot on which blood had been shed and prove that the spot was on American soil. The resolution was ignored in both Congress and the national papers, and it cost Lincoln political support in his district. One Illinois newspaper derisively nicknamed him "spotty Lincoln". Lincoln later regretted some of his statements, especially his attack on presidential war-making powers. Lincoln had pledged in 1846 to serve only one term in

2480-559: A large area of applied mathematics . Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete : An optimization problem can be represented in the following way: Such a formulation is called an optimization problem or a mathematical programming problem (a term not directly related to computer programming , but still in use for example in linear programming – see History below). Many real-world and theoretical problems may be modeled in this general framework. Since

2635-611: A leader of the new Republican Party . He reached a national audience in the 1858 Senate campaign debates against Stephen A. Douglas . Lincoln ran for president in 1860 , sweeping the North to gain victory. Pro-slavery elements in the South viewed his election as a threat to slavery, and Southern states began seceding from the nation . They formed the Confederate States of America, which began seizing federal military bases in

2790-436: A local maximum; finally, if indefinite, then the point is some kind of saddle point . Constrained problems can often be transformed into unconstrained problems with the help of Lagrange multipliers . Lagrangian relaxation can also provide approximate solutions to difficult constrained problems. Abraham Lincoln Abraham Lincoln ( / ˈ l ɪ ŋ k ən / LINK -ən ; February 12, 1809 – April 15, 1865)

2945-521: A matter of fact, their research suggests that a society with only two ethnic groups is about 50% more likely to experience civil war than either of the two extremes. Nonetheless, Mauro points out that ethno-linguistic fractionalization is positively correlated with corruption, which in turn is negatively correlated with economic growth. Moreover, in a study on economic growth in African countries, Easterly and Levine find that linguistic fractionalization plays

3100-618: A minimum from one that is a maximum or one that is neither. When the objective function is twice differentiable, these cases can be distinguished by checking the second derivative or the matrix of second derivatives (called the Hessian matrix ) in unconstrained problems, or the matrix of second derivatives of the objective function and the constraints called the bordered Hessian in constrained problems. The conditions that distinguish maxima, or minima, from other stationary points are called 'second-order conditions' (see ' Second derivative test '). If

3255-475: A new kind of "self-seeking capitalism" popularly known as Trumponomics could have a considerable impact on cross-border investment flows and long-term capital allocation The origins of modern development economics are often traced to the need for, and likely problems with the industrialization of eastern Europe in the aftermath of World War II. The key authors are Paul Rosenstein-Rodan , Kurt Mandelbaum , Ragnar Nurkse , and Sir Hans Wolfgang Singer . Only after

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3410-580: A patent for a flotation device for the movement of boats in shallow water. The idea was never commercialized, but it made Lincoln the only president to hold a patent. Lincoln appeared before the Illinois Supreme Court in 175 cases; he was sole counsel in 51 cases, of which 31 were decided in his favor. From 1853 to 1860, one of his largest clients was the Illinois Central Railroad . His legal reputation gave rise to

3565-430: A percentage of the population" as his measure of linguistic diversity. Not much later, however, Horowitz pointed out that both highly diverse and highly homogeneous societies exhibit less conflict than those in between. Similarly, Collier and Hoeffler provided evidence that both highly homogenous and highly heterogeneous societies exhibit lower risk of civil war, while societies that are more polarized are at greater risk. As

3720-451: A positive trade balance, protectionist measures such as tariffs and subsidies to home industries were advocated. Mercantilist development theory also advocated colonialism . Theorists most associated with mercantilism include Philipp von Hörnigk , who in his Austria Over All, If She Only Will of 1684 gave the only comprehensive statement of mercantilist theory, emphasizing production and an export-led economy. In France, mercantilist policy

3875-481: A rather ethnically homogeneous nation. However, civil war caused ethnicity (or ethnic affiliation) to be redefined according to clan groups. There is also much discussion in academia concerning the creation of an index for "ethnic heterogeneity". Several indices have been proposed in order to model ethnic diversity (with regards to conflict). Easterly and Levine have proposed an ethno-linguistic fractionalization index defined as FRAC or ELF defined by: where s i

4030-568: A reaction to the threat of modernization (perceived or actual) and neoliberal development. On a different note, Chua suggests that ethnic conflict often results from the envy of the majority toward a wealthy minority which has benefited from trade in a neoliberal world. She argues that conflict is likely to erupt through political manipulation and the vilification of the minority. Prasch points out that, as economic growth often occurs in tandem with increased inequality , ethnic or religious organizations may be seen as both assistance and an outlet for

4185-596: A significant role in reducing national income growth and in explaining poor policies. In addition, empirical research in the U.S. , at the municipal level, has revealed that ethnic fractionalization (based on race) may be correlated with poor fiscal management and lower investments in public goods . Finally, more recent research would propose that ethno-linguistic fractionalization is indeed negatively correlated with economic growth while more polarized societies exhibit greater public consumption, lower levels of investment and more frequent civil wars. Increasingly, attention

4340-497: A structural design, one would desire a design that is both light and rigid. When two objectives conflict, a trade-off must be created. There may be one lightest design, one stiffest design, and an infinite number of designs that are some compromise of weight and rigidity. The set of trade-off designs that improve upon one criterion at the expense of another is known as the Pareto set . The curve created plotting weight against stiffness of

4495-409: A substantial rise in inequality between internal regions of a country. The two-sector surplus model, which was developed in the 1950s, has been further criticized for its underlying assumption that predominantly agrarian societies suffer from a surplus of labor. Actual empirical studies have shown that such labor surpluses are only seasonal and drawing such labor to urban areas can result in a collapse of

4650-491: A success over a powerful Whig opponent. Then followed his four terms in the Illinois House of Representatives for Sangamon County . He championed construction of the Illinois and Michigan Canal , and later was a Canal Commissioner. He voted to expand suffrage beyond white landowners to all white males, but adopted a "free soil" stance opposing both slavery and abolition . In 1837, he declared, "[The] Institution of slavery

4805-546: A total of fewer than 12 months in aggregate by age 15. Nonetheless, he remained an avid reader and retained a lifelong interest in learning. Family, neighbors, and schoolmates recalled that his readings included the King James Bible , Aesop's Fables , John Bunyan 's The Pilgrim's Progress , Daniel Defoe 's Robinson Crusoe , and The Autobiography of Benjamin Franklin . Despite being self-educated, Lincoln

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4960-463: Is always necessary to continuously evaluate the quality of a data model by using a cost function where a minimum implies a set of possibly optimal parameters with an optimal (lowest) error. Typically, A is some subset of the Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , often specified by a set of constraints , equalities or inequalities that

5115-427: Is being drawn to the role of economics in spawning or cultivating ethnic conflict . Critics of earlier development theories, mentioned above, point out that "ethnicity" and ethnic conflict cannot be treated as exogenous variables. There is a body of literature that discusses how economic growth and development, particularly in the context of a globalizing world characterized by free trade , appears to be leading to

5270-455: Is delegated to the decision maker. In other words, defining the problem as multi-objective optimization signals that some information is missing: desirable objectives are given but combinations of them are not rated relative to each other. In some cases, the missing information can be derived by interactive sessions with the decision maker. Multi-objective optimization problems have been generalized further into vector optimization problems where

5425-678: Is founded on both injustice and bad policy, but the promulgation of abolition doctrines tends rather to increase than abate its evils." He echoed Henry Clay 's support for the American Colonization Society which advocated a program of abolition in conjunction with settling freed slaves in Liberia . He was admitted to the Illinois bar on September 9, 1836, and moved to Springfield and began to practice law under John T. Stuart , Mary Todd's cousin. Lincoln emerged as

5580-431: Is imperative, they argue, because future aid programs and policies to facilitate economic development must account for these differences. A growing body of research has been emerging among development economists since the very late 20th century focusing on interactions between ethnic diversity and economic development, particularly at the level of the nation-state . While most research looks at empirical economics at both

5735-444: Is in some developing countries, the discrepancy could be still bigger in a developed country where people may perform outside of financial transactions an even higher-value service than housekeeping or homebuilding as gifts or in their own households, such as counseling, lifestyle coaching , a more valuable home décor service, and time management. Even free choice can be considered to add value to lifestyles without necessarily increasing

5890-676: Is largely unproven; however recent advances in econometrics and more accurate measurements in many countries are creating new knowledge by compensating for the effects of variables to determine probable causes out of merely correlational statistics. Recent theories revolve around questions about what variables or inputs correlate or affect economic growth the most: elementary, secondary, or higher education, government policy stability, tariffs and subsidies, fair court systems, available infrastructure, availability of medical care, prenatal care and clean water, ease of entry and exit into trade, and equality of income distribution (for example, as indicated by

6045-502: Is most associated with 17th-century finance minister Jean-Baptiste Colbert , whose policies proved influential in later American development. Mercantilist ideas continue in the theories of economic nationalism and neomercantilism . Following mercantilism was the related theory of economic nationalism , promulgated in the 19th century related to the development and industrialization of the United States and Germany, notably in

6200-422: Is much economic activity that is not part of measured financial transactions (such as housekeeping and self-homebuilding), or where funding is not available for accurate measurements to be made publicly available for other economists to use in their studies (including private and institutional fraud, in some countries). Even though per-capita GDP as measured can make economic well-being appear smaller than it really

6355-441: Is no consensus on what students should know. Different approaches may consider the factors that contribute to economic convergence or non-convergence across households, regions, and countries. The earliest Western theory of development economics was mercantilism , which developed in the 17th century, paralleling the rise of the nation state . Earlier theories had given little attention to development. For example, scholasticism ,

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6510-404: Is no such maximum as the objective function is unbounded, so the answer is " infinity " or " undefined ". Consider the following notation: or equivalently This represents the value (or values) of the argument x in the interval (−∞,−1] that minimizes (or minimize) the objective function x + 1 (the actual minimum value of that function is not what the problem asks for). In this case,

6665-509: Is not guaranteed that different solutions will be obtained even with different starting points in multiple runs of the algorithm. Common approaches to global optimization problems, where multiple local extrema may be present include evolutionary algorithms , Bayesian optimization and simulated annealing . The satisfiability problem , also called the feasibility problem , is just the problem of finding any feasible solution at all without regard to objective value. This can be regarded as

6820-461: Is null or negative. The extreme value theorem of Karl Weierstrass states that a continuous real-valued function on a compact set attains its maximum and minimum value. More generally, a lower semi-continuous function on a compact set attains its minimum; an upper semi-continuous function on a compact set attains its maximum point or view. One of Fermat's theorems states that optima of unconstrained problems are found at stationary points , where

6975-628: Is size of group i as a percentage of total population. The ELF index is a measure of the probability that two randomly chosen individuals belong to different ethno-linguistic groups. Other researchers have also applied this index to religious rather than ethno-linguistic groups. Though commonly used, Alesina and La Ferrara point out that the ELF index fails to account for the possibility that fewer large ethnic groups may result in greater inter-ethnic conflict than many small ethnic groups. More recently, researchers such as Montalvo and Reynal-Querol, have put forward

7130-460: Is the strong man of the party ... and if I beat him, my victory will be hardly won." The Senate campaign featured seven debates between Lincoln and Douglas. These were the most famous political debates in American history; they had an atmosphere akin to a prizefight and drew crowds in the thousands. The principals stood in stark contrast both physically and politically. Lincoln warned that

7285-402: Is thought to be – at least to some degree – religiously based. Some have proposed that, as the saliency of these different ethnic variables tends to vary over time and across geography, research methodologies should vary according to the context. Somalia provides an interesting example. Due to the fact that about 85% of its population defined themselves as Somali , Somalia was considered to be

7440-618: Is to say that this early and simplistic theory failed to account for political, social, and institutional obstacles to development. Furthermore, this theory was developed in the early years of the Cold War and was largely derived from the successes of the Marshall Plan . This has led to the major criticism that the theory assumes that the conditions found in developing countries are the same as those found in post-WWII Europe. Structural-change theory deals with policies focused on changing

7595-427: Is very uncertain. Countries that maintain stability can experience a "peace dividend," through the rapid re-accumulation of physical capital (investment flows back to the recovering country because of the high return). However, successful recovery depends on the quality of legal system and the protection of private property. Investment is more productive in countries with higher quality institutions. Firms that experienced

7750-505: The Gini coefficient ), and how to advise governments about macroeconomic policies, which include all policies that affect the economy. Education enables countries to adapt the latest technology and creates an environment for new innovations. The cause of limited growth and divergence in economic growth lies in the high rate of acceleration of technological change by a small number of developed countries. These countries' acceleration of technology

7905-539: The Illinois Militia during the Black Hawk War . When Lincoln returned home from the Black Hawk War , he planned to become a blacksmith, but instead formed a partnership with 21-year-old William Berry, with whom he purchased a New Salem general store on credit. Because a license was required to sell customers beverages, Berry obtained bartending licenses for $ 7 each for Lincoln and himself, and in 1833

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8060-488: The Lincoln-Berry General Store became a tavern as well. As licensed bartenders, Lincoln and Berry were able to sell spirits, including liquor, for 12 cents a pint. They offered a wide range of alcoholic beverages as well as food, including takeout dinners. But Berry became an alcoholic, was often too drunk to work, and Lincoln ended up running the store by himself. Although the economy was booming,

8215-441: The Q polarization index as a more appropriate measure of ethnic division. Based on a simplified adaptation of a polarization index developed by Esteban and Ray, the Q index is defined as where s i once again represents the size of group i as a percentage of total population, and is intended to capture the social distance between existing ethnic groups within an area. Early researchers, such as Jonathan Pool, considered

8370-636: The Slave Power was threatening the values of republicanism, and he accused Douglas of distorting the Founding Fathers' premise that all men are created equal . In his Freeport Doctrine , Douglas argued that, despite the Dred Scott decision, which he claimed to support, local settlers, under the doctrine of popular sovereignty , should be free to choose whether to allow slavery within their territory, and he accused Lincoln of having joined

8525-646: The War Democrats and the Radical Republicans , demanded harsh treatment of the Southern Confederates. He managed the factions by exploiting their mutual enmity, carefully distributing political patronage, and by appealing to the American people. Anti-war Democrats (called " Copperheads ") despised Lincoln, and some irreconcilable pro-Confederate elements went so far as to plot his assassination. His Gettysburg Address became one of

8680-857: The market-friendly approach . Of the three, both the free-market approach and public-choice theory contend that the market should be totally free, meaning that any intervention by the government is necessarily bad. Public-choice theory is arguably the more radical of the two with its view, closely associated with libertarianism , that governments themselves are rarely good and therefore should be as minimal as possible. Academic economists have given varied policy advice to governments of developing countries. See for example, Economy of Chile ( Arnold Harberger ), Economic history of Taiwan ( Sho-Chieh Tsiang ). Anne Krueger noted in 1996 that success and failure of policy recommendations worldwide had not consistently been incorporated into prevailing academic writings on trade and development. The market-friendly approach, unlike

8835-411: The "sequential process through which the economic, industrial, and institutional structure of an underdeveloped economy is transformed over time to permit new industries to replace traditional agriculture as the engine of economic growth." Structural-change approaches to development economics have faced criticism for their emphasis on urban development at the expense of rural development which can lead to

8990-595: The (partial) ordering is no longer given by the Pareto ordering. Optimization problems are often multi-modal; that is, they possess multiple good solutions. They could all be globally good (same cost function value) or there could be a mix of globally good and locally good solutions. Obtaining all (or at least some of) the multiple solutions is the goal of a multi-modal optimizer. Classical optimization techniques due to their iterative approach do not perform satisfactorily when they are used to obtain multiple solutions, since it

9145-555: The 1858 election, newspapers frequently mentioned Lincoln as a potential Republican presidential candidate, rivaled by William H. Seward , Salmon P. Chase , Edward Bates , and Simon Cameron . While Lincoln was popular in the Midwest, he lacked support in the Northeast and was unsure whether to seek the office. In January 1860, Lincoln told a group of political allies that he would accept the presidential nomination if offered and, in

9300-533: The American economist Henry Clay . Hamilton's 1791 Report on Manufactures , his magnum opus , is the founding text of the American System, and drew from the mercantilist economies of Britain under Elizabeth I and France under Colbert. List's 1841 Das Nationale System der Politischen Ökonomie (translated into English as The National System of Political Economy), which emphasized stages of growth. Hamilton professed that developing an industrialized economy

9455-608: The House. Realizing Clay was unlikely to win the presidency, he supported General Zachary Taylor for the Whig nomination in the 1848 presidential election . Taylor won and Lincoln hoped in vain to be appointed Commissioner of the United States General Land Office . The administration offered to appoint him secretary or governor of the Oregon Territory as consolation. This distant territory

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9610-555: The Know-Nothings nominated former Whig President Millard Fillmore . Buchanan prevailed, while Republican William Henry Bissell won election as Governor of Illinois, and Lincoln became a leading Republican in Illinois. Dred Scott was a slave whose master took him from a slave state to a territory that was free as a result of the Missouri Compromise . After Scott was returned to the slave state, he petitioned

9765-573: The Moon was at a low angle, drastically reducing visibility. Armstrong was acquitted. In an 1859 murder case, leading up to his presidential campaign, Lincoln elevated his profile with his defense of Simeon Quinn "Peachy" Harrison, who was a third cousin; Harrison was also the grandson of Lincoln's political opponent, Rev. Peter Cartwright . Harrison was charged with the murder of Greek Crafton who, as he lay dying of his wounds, confessed to Cartwright that he had provoked Harrison. Lincoln angrily protested

9920-748: The New York Tribune, at that time wrote up an unflattering account of Lincoln's compromising position on slavery and his reluctance to challenge the court's Dred Scott ruling, which was promptly used against him by his political rivals. On February 27, 1860, powerful New York Republicans invited Lincoln to give a speech at Cooper Union , in which he argued that the Founding Fathers of the United States had little use for popular sovereignty and had repeatedly sought to restrict slavery. He insisted that morality required opposition to slavery and rejected any "groping for some middle ground between

10075-472: The ODI suggest growth is necessary, but that it must be equitable. This concept of inclusive growth is shared even by key world leaders such as former Secretary General Ban Ki-moon , who emphasises that: Researchers at the ODI thus emphasise the need to ensure social protection is extended to allow universal access and that active policy measures are introduced to encourage the private sector to create new jobs as

10230-595: The South. A little over one month after Lincoln assumed the presidency, Confederate forces attacked Fort Sumter , a U.S. fort in South Carolina. Following the bombardment, Lincoln mobilized forces to suppress the rebellion and restore the union. Lincoln, a moderate Republican , had to navigate a contentious array of factions with friends and opponents from both the Democratic and Republican parties. His allies,

10385-514: The U.S. as a nation. "It cannot come from abroad. If destruction be our lot, we must ourselves be its author and finisher", said Lincoln. Prior to that, on April 28, 1836, a black man, Francis McIntosh , was burned alive in St. Louis , Missouri . Zann Gill describes how these two murders set off a chain reaction that ultimately prompted Abraham Lincoln to run for President. True to his record, Lincoln professed to friends in 1861 to be "an old line Whig,

10540-643: The Union and abolish slavery. He is often ranked in both popular and scholarly polls as the greatest president in American history. Abraham Lincoln was born on February 12, 1809, the second child of Thomas Lincoln and Nancy Hanks Lincoln , in a log cabin on Sinking Spring Farm near Hodgenville, Kentucky . He was a descendant of Samuel Lincoln , an Englishman who migrated from Hingham, Norfolk , to its namesake, Hingham, Massachusetts , in 1638. The family through subsequent generations migrated west, passing through New Jersey , Pennsylvania , and Virginia . Lincoln

10695-399: The Union to be dissolved—I do not expect the house to fall—but I do expect it will cease to be divided. It will become all one thing, or all the other." The speech created a stark image of the danger of disunion. The stage was then set for the election of the Illinois legislature which would, in turn, select Lincoln or Douglas. When informed of Lincoln's nomination, Douglas stated, "[Lincoln]

10850-533: The Whigs were irreparably split by the Kansas–Nebraska Act and other efforts to compromise on the slavery issue. Reflecting on the demise of his party, Lincoln wrote in 1855, "I think I am a Whig, but others say there are no Whigs, and that I am an abolitionist. ... I do no more than oppose the extension of slavery." The new Republican Party was formed as a northern party dedicated to antislavery, drawing from

11005-516: The abolitionists. Lincoln's argument assumed a moral tone, as he claimed that Douglas represented a conspiracy to promote slavery. Douglas's argument was more legal in nature, claiming that Lincoln was defying the authority of the U.S. Supreme Court as exercised in the Dred Scott decision. Though the Republican legislative candidates won more popular votes, the Democrats won more seats, and

11160-436: The accelerated accumulation of capital, through the utilization of both domestic and international savings as a means of spurring investment, as the primary means of promoting economic growth and, thus, development. The linear-stages-of-growth model posits that there are a series of five consecutive stages of development that all countries must go through during the process of development. These stages are "the traditional society,

11315-801: The agricultural sector. The patterns of development approach has been criticized for lacking a theoretical framework. International dependence theories gained prominence in the 1970s as a reaction to the failure of earlier theories to lead to widespread successes in international development . Unlike earlier theories, international dependence theories have their origins in developing countries and view obstacles to development as being primarily external in nature, rather than internal. These theories view developing countries as being economically and politically dependent on more powerful, developed countries that have an interest in maintaining their dominant position. There are three different, major formulations of international dependence theory: neocolonial dependence theory,

11470-439: The allocation of resources occurs with the greatest efficiency possible and that economic growth is raised and stabilized. There are several different approaches within the realm of neoclassical theory, each with subtle, but important, differences in their views regarding the extent to which the market should be left unregulated. These different takes on neoclassical theory are the free market approach , public-choice theory , and

11625-411: The answer is x = −1 , since x = 0 is infeasible, that is, it does not belong to the feasible set . Similarly, or equivalently represents the { x , y } pair (or pairs) that maximizes (or maximize) the value of the objective function x cos y , with the added constraint that x lie in the interval [−5,5] (again, the actual maximum value of the expression does not matter). In this case,

11780-467: The antislavery wing of the Whig Party and combining Free Soil , Liberty , and antislavery Democratic Party members, Lincoln resisted early Republican entreaties, fearing that the new party would become a platform for extreme abolitionists. Lincoln held out hope for rejuvenating the Whigs, though he lamented his party's growing closeness with the nativist Know Nothing movement. In 1854, Lincoln

11935-408: The best designs is known as the Pareto frontier . A design is judged to be "Pareto optimal" (equivalently, "Pareto efficient" or in the Pareto set) if it is not dominated by any other design: If it is worse than another design in some respects and no better in any respect, then it is dominated and is not Pareto optimal. The choice among "Pareto optimal" solutions to determine the "favorite solution"

12090-468: The business struggled and went into debt, causing Lincoln to sell his share. In his first campaign speech after returning from his military service, Lincoln observed a supporter in the crowd under attack, grabbed the assailant by his "neck and the seat of his trousers", and tossed him. In the campaign, Lincoln advocated for navigational improvements on the Sangamon River . He could draw crowds as

12245-512: The continuity of an optimal solution as a function of underlying parameters. For unconstrained problems with twice-differentiable functions, some critical points can be found by finding the points where the gradient of the objective function is zero (that is, the stationary points). More generally, a zero subgradient certifies that a local minimum has been found for minimization problems with convex functions and other locally Lipschitz functions , which meet in loss function minimization of

12400-476: The developed world during the 1980s, neoclassical theories represent a radical shift away from International Dependence Theories. Neoclassical theories argue that governments should not intervene in the economy; in other words, these theories are claiming that an unobstructed free market is the best means of inducing rapid and successful development. Competitive free markets unrestrained by excessive government regulation are seen as being able to naturally ensure that

12555-458: The development of an urbanized industrial sector, and Hollis Chenery's patterns of development approach, which holds that different countries become wealthy via different trajectories. The pattern that a particular country will follow, in this framework, depends on its size and resources, and potentially other factors including its current income level and comparative advantages relative to other nations. Empirical analysis in this framework studies

12710-408: The development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes

12865-412: The disadvantaged. However, empirical research by Piazza argues that economics and unequal development have little to do with social unrest in the form of terrorism . Rather, "more diverse societies, in terms of ethnic and religious demography , and political systems with large, complex, multiparty systems were more likely to experience terrorism than were more homogeneous states with few or no parties at

13020-569: The dispute over slavery in the territories, the decision sparked further outrage in the North. Lincoln denounced it as the product of a conspiracy of Democrats to support the Slave Power . He argued the decision was at variance with the Declaration of Independence; he said that while the founding fathers did not believe all men equal in every respect, they believed all men were equal "in certain inalienable rights, among which are life, liberty, and

13175-406: The dominant school of thought during medieval feudalism, emphasized reconciliation with Christian theology and ethics, rather than development. The 16th- and 17th-century School of Salamanca , credited as the earliest modern school of economics, likewise did not address development specifically. Major European nations in the 17th and 18th centuries all adopted mercantilist ideals to varying degrees,

13330-417: The early 1830s, he met Mary Owens from Kentucky. Late in 1836, Lincoln agreed to a match with Owens if she returned to New Salem. Owens arrived that November and he courted her; however, they both had second thoughts. On August 16, 1837, he wrote Owens a letter saying he would not blame her if she ended the relationship, and she never replied. In 1839, Lincoln met Mary Todd in Springfield, Illinois , and

13485-424: The economic structures of developing countries from being composed primarily of subsistence agricultural practices to being a "more modern, more urbanized, and more industrially diverse manufacturing and service economy." There are two major forms of structural-change theory: W. Lewis' two-sector surplus model , which views agrarian societies as consisting of large amounts of surplus labor which can be utilized to spur

13640-596: The economy grows (as opposed to jobless growth ) and seek to employ people from disadvantaged groups. Optimization (mathematics) Mathematical optimization (alternatively spelled optimisation ) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization . Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics , and

13795-753: The extended Lincoln family, including Abraham, moved west to Illinois, a free state, and settled in Macon County . Abraham then became increasingly distant from Thomas, in part, due to his father's lack of interest in education. In 1831, as Thomas and other family members prepared to move to a new homestead in Coles County, Illinois , Abraham struck out on his own. He made his home in New Salem, Illinois , for six years. Lincoln and some friends took goods, including live hogs, by flatboat to New Orleans, Louisiana , where he first witnessed slavery. Speculation persists that Lincoln's first romantic interest

13950-445: The extinction and homogenization of languages. Manuel Castells asserts that the "widespread destructuring of organizations, delegitimation of institutions, fading away of major social movements, and ephemeral cultural expressions" which characterize globalization lead to a renewed search for meaning; one that is based on identity rather than on practices. Barber and Lewis argue that culturally-based movements of resistance have emerged as

14105-486: The false-paradigm model, and the dualistic-dependence model. The first formulation of international dependence theory, neocolonial dependence theory, has its origins in Marxism and views the failure of many developing nations to undergo successful development as being the result of the historical development of the international capitalist system. First gaining prominence with the rise of several conservative governments in

14260-551: The family moved to Indiana , where the land surveys and titles were more reliable. They settled in an "unbroken forest" in Hurricane Township, Perry County, Indiana . When the Lincolns moved to Indiana it "had just been admitted to the Union" as a "free" (non-slaveholding) state, except that, though "no new enslaved people were allowed, ... currently enslaved individuals remained so". In 1860, Lincoln noted that

14415-695: The family settled in Hardin County, Kentucky , in the early 1800s. Lincoln's mother Nancy Lincoln is widely assumed to be the daughter of Lucy Hanks. Thomas and Nancy married on June 12, 1806, in Washington County, and moved to Elizabethtown, Kentucky . They had three children: Sarah , Abraham, and Thomas, who died as an infant. Thomas Lincoln bought multiple farms in Kentucky, but could not get clear property titles to any, losing hundreds of acres of land in property disputes. In 1816,

14570-834: The family's move to Indiana was "partly on account of slavery", but mainly due to land title difficulties. In Kentucky and Indiana, Thomas worked as a farmer, cabinetmaker, and carpenter. At various times he owned farms, livestock, and town lots, paid taxes, sat on juries, appraised estates, and served on county patrols. Thomas and Nancy were members of a Separate Baptist Church , which "condemned profanity, intoxication, gossip, horse racing, and dancing." Most of its members opposed slavery. Overcoming financial challenges, Thomas in 1827 obtained clear title to 80 acres (32 ha) in Indiana, an area that became known as Little Pigeon Creek Community . On October 5, 1818, Nancy Lincoln died from milk sickness , leaving 11-year-old Sarah in charge of

14725-485: The financial transaction amounts. More recent theories of Human Development have begun to see beyond purely financial measures of development, for example with measures such as medical care available, education, equality, and political freedom. One measure used is the Genuine Progress Indicator , which relates strongly to theories of distributive justice . Actual knowledge about what creates growth

14880-403: The first derivative or the gradient of the objective function is zero (see first derivative test ). More generally, they may be found at critical points , where the first derivative or gradient of the objective function is zero or is undefined, or on the boundary of the choice set. An equation (or set of equations) stating that the first derivative(s) equal(s) zero at an interior optimum is called

15035-413: The first six rounds of voting, he was unable to obtain a majority. Lincoln instructed his backers to vote for Lyman Trumbull . Trumbull was an antislavery Democrat and had received few votes in the earlier ballots; his supporters, also antislavery Democrats, had vowed not to support any Whig. Lincoln's decision to withdraw enabled his Whig supporters and Trumbull's antislavery Democrats to combine and defeat

15190-453: The first time, Illinois Republicans held a convention to agree upon a Senate candidate, and Lincoln won the nomination with little opposition. Lincoln accepted the nomination with great enthusiasm and zeal. After his nomination he delivered his House Divided Speech , with the biblical reference Mark 3:25 , "A house divided against itself cannot stand. I believe this government cannot endure permanently half slave and half free. I do not expect

15345-425: The following is valid: it suffices to solve only minimization problems. However, the opposite perspective of considering only maximization problems would be valid, too. Problems formulated using this technique in the fields of physics may refer to the technique as energy minimization , speaking of the value of the function f as representing the energy of the system being modeled . In machine learning , it

15500-490: The following months, several local papers endorsed his candidacy. Over the coming months Lincoln was tireless, making nearly fifty speeches along the campaign trail. By the quality and simplicity of his rhetoric, he quickly became the champion of the Republican party. However, despite his overwhelming support in the Midwestern United States , he was less appreciated in the east. Horace Greeley , editor of

15655-411: The following notation: This denotes the minimum value of the objective function x + 1 , when choosing x from the set of real numbers R {\displaystyle \mathbb {R} } . The minimum value in this case is 1, occurring at x = 0 . Similarly, the notation asks for the maximum value of the objective function 2 x , where x may be any real number. In this case, there

15810-518: The following year they became engaged. She was the daughter of Robert Smith Todd , a wealthy lawyer and businessman in Lexington, Kentucky . Their wedding, which was set for January 1, 1841, was canceled because Lincoln did not appear, but they reconciled and married on November 4, 1842, in the Springfield home of Mary's sister. While anxiously preparing for the nuptials, he was asked where he

15965-425: The former as actual solutions to the original problem. Global optimization is the branch of applied mathematics and numerical analysis that is concerned with the development of deterministic algorithms that are capable of guaranteeing convergence in finite time to the actual optimal solution of a nonconvex problem. Optimization problems are often expressed with special notation. Here are some examples: Consider

16120-612: The functions of such organisations as the International Monetary Fund and World Bank . In fact, the majority of development economists are employed by, do consulting with, or receive funding from institutions like the IMF and the World Bank. Many such economists are interested in ways of promoting stable and sustainable growth in poor countries and areas, by promoting domestic self-reliance and education in some of

16275-490: The human condition, raising people out of poverty and achieving the Millennium Development Goals . Despite research showing almost no relation between growth and the achievement of the goals 2 to 7 and statistics showing that during periods of growth poverty levels in some cases have actually risen (e.g. Uganda grew by 2.5% annually between 2000 and 2003, yet poverty levels rose by 3.8%), researchers at

16430-532: The influence of economist Henry Charles Carey . Forms of economic nationalism and neomercantilism have also been key in Japan's development in the 19th and 20th centuries, and the more recent development of the Four Asian Tigers (Hong Kong, South Korea, Taiwan, and Singapore), and, most significantly, China. Following Brexit and the 2016 United States presidential election , some experts have argued

16585-545: The influence only ebbing with the 18th-century development of physiocrats in France and classical economics in Britain. Mercantilism held that a nation's prosperity depended on its supply of capital, represented by bullion (gold, silver, and trade value) held by the state. It emphasised the maintenance of a high positive trade balance (maximising exports and minimising imports) as a means of accumulating this bullion. To achieve

16740-570: The issue of endogeneity (endogenicity) into questions. This remains a highly contested and uncertain field of research, as well as politically sensitive, largely due to its possible policy implications. Much discussion among researchers centers around defining and measuring two key but related variables: ethnicity and diversity . It is debated whether ethnicity should be defined by culture, language, or religion. While conflicts in Rwanda were largely along tribal lines, Nigeria's string of conflicts

16895-474: The judge's initial decision to exclude Cartwright's testimony about the confession as inadmissible hearsay . Lincoln argued that the testimony involved a dying declaration and was not subject to the hearsay rule. Instead of holding Lincoln in contempt of court as expected, the judge, a Democrat, reversed his ruling and admitted the testimony into evidence, resulting in Harrison's acquittal. The debate over

17050-412: The label of "The Rail Candidate". In 1860, Lincoln described himself: "I am in height, six feet, four inches, nearly; lean in flesh, weighing, on an average, one hundred and eighty pounds; dark complexion, with coarse black hair, and gray eyes." Michael Martinez wrote about the effective imaging of Lincoln by his campaign. At times he was presented as the plain-talking "Rail Splitter" and at other times he

17205-448: The law office. Their father, it seemed, was often too absorbed in his work to notice his children's behavior. Herndon recounted, "I have felt many and many a time that I wanted to wring their little necks, and yet out of respect for Lincoln I kept my mouth shut. Lincoln did not note what his children were doing or had done." The deaths of their sons Eddie and Willie had profound effects on both parents. Lincoln suffered from " melancholy ",

17360-540: The legislature re-elected Douglas. However, Lincoln's articulation of the issues had given him a national political presence. In May 1859, Lincoln purchased the Illinois Staats-Anzeiger , a German-language newspaper that was consistently supportive; most of the state's 130,000 German Americans voted for Democrats, but the German-language paper mobilized Republican support. In the aftermath of

17515-501: The lowest income countries in the world. Where economic issues merge with social and political ones, it is referred to as development studies . Economists Jeffrey D. Sachs , Andrew Mellinger, and John Gallup argue that a nation's geographical location and topography are key determinants and predictors of its economic prosperity. Areas developed along the coast and near "navigable waterways" are far wealthier and more densely populated than those further inland. Furthermore, countries outside

17670-450: The macro and the micro level, this field of study has a particularly heavy sociological approach. The more conservative branch of research focuses on tests for causality in the relationship between different levels of ethnic diversity and economic performance, while a smaller and more radical branch argues for the role of neoliberal economics in enhancing or causing ethnic conflict . Moreover, comparing these two theoretical approaches brings

17825-708: The mainstream Democratic candidate, Joel Aldrich Matteson . Violent political confrontations in Kansas continued, and opposition to the Kansas–Nebraska Act remained strong throughout the North. As the 1856 elections approached, Lincoln joined the Republicans and attended the Bloomington Convention , which formally established the Illinois Republican Party . The convention platform endorsed Congress's right to regulate slavery in

17980-510: The members of A have to satisfy. The domain A of f is called the search space or the choice set , while the elements of A are called candidate solutions or feasible solutions . The function f is variously called an objective function , criterion function , loss function , cost function (minimization), utility function or fitness function (maximization), or, in certain fields, an energy function or energy functional . A feasible solution that minimizes (or maximizes)

18135-478: The midst of the nation's western expansion, particularly river barge conflicts under the many new railroad bridges. As a riverboat man, Lincoln initially favored those interests, but ultimately represented whoever hired him. He later represented a bridge company against a riverboat company in Hurd v. Rock Island Bridge Company , a landmark case involving a canal boat that sank after hitting a bridge. In 1849 he received

18290-597: The most famous speeches in American history. Lincoln closely supervised the strategy and tactics in the war effort, including the selection of generals, and implemented a naval blockade of the South's trade. He suspended habeas corpus in Maryland and elsewhere , and he averted war with Britain by defusing the Trent Affair . In 1863, he issued the Emancipation Proclamation , which declared

18445-434: The national level". Violent conflict and economic development are deeply intertwined. Paul Collier describes how poor countries are more prone to civil conflict. The conflict lowers incomes catching countries in a "conflict trap." Violent conflict destroys physical capital (equipment and infrastructure), diverts valuable resources to military spending, discourages investment and disrupts exchange. Recovery from civil conflict

18600-456: The neural network. The positive-negative momentum estimation lets to avoid the local minimum and converges at the objective function global minimum. Further, critical points can be classified using the definiteness of the Hessian matrix : If the Hessian is positive definite at a critical point, then the point is a local minimum; if the Hessian matrix is negative definite, then the point is

18755-410: The nickname "Honest Abe". In an 1858 criminal trial, Lincoln represented William "Duff" Armstrong, who was on trial for the murder of James Preston Metzker. The case is famous for Lincoln's use of a fact established by judicial notice to challenge the credibility of an eyewitness. After an opposing witness testified to seeing the crime in the moonlight, Lincoln produced a Farmers' Almanac showing

18910-621: The nomination in 1846, but also won the election. He was the only Whig in the Illinois delegation, but as dutiful as any participated in almost all votes and made speeches that toed the party line. He was assigned to the Committee on Post Office and Post Roads and the Committee on Expenditures in the War Department . Lincoln teamed with Joshua R. Giddings on a bill to abolish slavery in the District of Columbia with compensation for

19065-406: The objective function is called an optimal solution . In mathematics, conventional optimization problems are usually stated in terms of minimization. A local minimum x * is defined as an element for which there exists some δ > 0 such that the expression f ( x *) ≤ f ( x ) holds; that is to say, on some region around x * all of the function values are greater than or equal to

19220-401: The office of an established attorney, as was the custom, Lincoln borrowed legal texts from attorneys John Todd Stuart and Thomas Drummond , purchased books including Blackstone 's Commentaries and Chitty 's Pleadings , and read law on his own. He later said of his legal education that "I studied with nobody." Lincoln's second state house campaign in 1834, this time as a Whig , was

19375-461: The other two, is a more recent development and is often associated with the World Bank . This approach still advocates free markets but recognizes that there are many imperfections in the markets of many developing nations and thus argues that some government intervention is an effective means of fixing such imperfections. Development economics also includes topics such as third world debt , and

19530-705: The owners, enforcement to capture fugitive slaves, and a popular vote on the matter. He dropped the bill when it eluded Whig support. On foreign and military policy, Lincoln spoke against the Mexican–American War , which he imputed President James K. Polk 's desire for "military glory — that attractive rainbow, that rises in showers of blood". He supported the Wilmot Proviso , a failed proposal to ban slavery in any U.S. territory won from Mexico. Lincoln emphasized his opposition to Polk by drafting and introducing his Spot Resolutions . The war had begun with

19685-802: The policies of the American System in America and the Zollverein (customs union) in Germany. A significant difference from mercantilism was the de-emphasis on colonies, in favor of a focus on domestic production. The names most associated with 19th-century economic nationalism are the first United States Secretary of the Treasury Alexander Hamilton , the German-American Friedrich List , and

19840-479: The pre-conditions for take-off, the take-off, the drive to maturity, and the age of high mass-consumption" Simple versions of the Harrod–Domar model provide a mathematical illustration of the argument that improved capital investment leads to greater economic growth. Such theories have been criticized for not recognizing that, while necessary, capital accumulation is not a sufficient condition for development. That

19995-475: The presidency. He said the Kansas Act had a " declared indifference, but as I must think, a covert real zeal for the spread of slavery. I cannot but hate it. I hate it because of the monstrous injustice of slavery itself. I hate it because it deprives our republican example of its just influence in the world...." Lincoln's attacks on the Kansas–Nebraska Act marked his return to political life. Nationally

20150-552: The pursuit of happiness". In 1858, Douglas was up for re-election in the U.S. Senate, and Lincoln hoped to defeat him. Many in the party felt that a former Whig should be nominated in 1858, and Lincoln's 1856 campaigning and support of Trumbull had earned him a favor. Some eastern Republicans supported Douglas for his opposition to the Lecompton Constitution and admission of Kansas as a slave state . Many Illinois Republicans resented this eastern interference. For

20305-527: The right and the wrong". Many in the audience thought he appeared awkward and even ugly. But Lincoln demonstrated intellectual leadership, which brought him into contention. Journalist Noah Brooks reported, "No man ever before made such an impression on his first appeal to a New York audience". Historian David Herbert Donald described the speech as "a superb political move for an unannounced presidential aspirant. Appearing in Seward's home state, sponsored by

20460-419: The set of feasible elements), it is also the global minimum, but a nonconvex problem may have more than one local minimum not all of which need be global minima. A large number of algorithms proposed for solving the nonconvex problems – including the majority of commercially available solvers – are not capable of making a distinction between locally optimal solutions and globally optimal solutions, and will treat

20615-589: The slaves in the states "in rebellion" to be free. It also directed the Army and Navy to "recognize and maintain the freedom of said persons" and to receive them "into the armed service of the United States." Lincoln pressured border states to outlaw slavery, and he promoted the Thirteenth Amendment to the U.S. Constitution , which abolished slavery, except as punishment for a crime. Lincoln managed his own successful re-election campaign . He sought to heal

20770-509: The solutions are the pairs of the form {5, 2 k π } and {−5, (2 k + 1) π } , where k ranges over all integers . Operators arg min and arg max are sometimes also written as argmin and argmax , and stand for argument of the minimum and argument of the maximum . Fermat and Lagrange found calculus-based formulae for identifying optima, while Newton and Gauss proposed iterative methods for moving towards an optimum. The term " linear programming " for certain optimization cases

20925-405: The special case of mathematical optimization where the objective value is the same for every solution, and thus any solution is optimal. Many optimization algorithms need to start from a feasible point. One way to obtain such a point is to relax the feasibility conditions using a slack variable ; with enough slack, any starting point is feasible. Then, minimize that slack variable until the slack

21080-654: The status of slavery in the territories failed to alleviate tensions between the slave-holding South and the free North, with the failure of the Compromise of 1850 , a legislative package designed to address the issue. In his 1852 eulogy for Clay, Lincoln highlighted the latter's support for gradual emancipation and opposition to "both extremes" on the slavery issue. As the slavery debate in the Nebraska and Kansas territories became particularly acrimonious, Illinois Senator Stephen A. Douglas proposed popular sovereignty as

21235-529: The territories and backed the admission of Kansas as a free state. Lincoln gave the final speech of the convention supporting the party platform and called for the preservation of the Union. At the June 1856 Republican National Convention , though Lincoln received support to run as vice president, John C. Frémont and William Dayton were on the ticket, which Lincoln supported throughout Illinois. The Democrats nominated former Secretary of State James Buchanan and

21390-422: The theoretical aspects of linear programming (like the theory of duality ) around the same time. Other notable researchers in mathematical optimization include the following: In a number of subfields, the techniques are designed primarily for optimization in dynamic contexts (that is, decision making over time): Adding more than one objective to an optimization problem adds complexity. For example, to optimize

21545-506: The tropic zones, which have more temperate climates, have also developed considerably more than those located within the Tropic of Cancer and the Tropic of Capricorn . These climates outside the tropic zones, described as "temperate-near," hold roughly a quarter of the world's population and produce more than half of the world's GNP, yet account for only 8.4% of the world's inhabited area. Understanding of these different geographies and climates

21700-400: The value at that element. Local maxima are defined similarly. While a local minimum is at least as good as any nearby elements, a global minimum is at least as good as every feasible element. Generally, unless the objective function is convex in a minimization problem, there may be several local minima. In a convex problem , if there is a local minimum that is interior (not on the edge of

21855-598: The war did economists turn their concerns towards Asia, Africa, and Latin America. At the heart of these studies, by authors such as Simon Kuznets and W. Arthur Lewis was an analysis of not only economic growth but also structural transformation. An early theory of development economics, the linear-stages-of-growth model was first formulated in the 1950s by W. W. Rostow in The Stages of Growth: A Non-Communist Manifesto, following work of Marx and List. This theory modifies Marx's stages theory of development and focuses on

22010-523: The war-torn nation through reconciliation. On April 14, 1865, just five days after the Confederate surrender at Appomattox , he was attending a play at Ford's Theatre in Washington, D.C., with his wife, Mary , when he was fatally shot by Confederate sympathizer John Wilkes Booth . Lincoln is remembered as a martyr and a national hero for his wartime leadership and for his efforts to preserve

22165-485: Was Ann Rutledge , whom he met when he moved to New Salem. However, witness testimony, given decades afterward, showed a lack of any specific recollection of a romance between the two. Rutledge died on August 25, 1835, most likely of typhoid fever ; Lincoln took the death very hard, saying that he could not bear the idea of rain falling on Ann's grave. Lincoln sank into a serious episode of depression, and this gave rise to speculation that he had been in love with her. In

22320-503: Was a Democratic stronghold, and acceptance of the post would have disrupted his legal and political career in Illinois, so he declined and resumed his law practice. In his Springfield practice, Lincoln handled "every kind of business that could come before a prairie lawyer". Twice a year he appeared for 10 consecutive weeks in county seats in the Midstate county courts; this continued for 16 years. Lincoln handled transportation cases in

22475-550: Was also a descendant of the Harrison family of Virginia ; his paternal grandfather and namesake, Captain Abraham Lincoln and wife Bathsheba (née Herring) moved the family from Virginia to Jefferson County, Kentucky . The captain was killed in an Indian raid in 1786. His children, including eight-year-old Thomas, Abraham's father, witnessed the attack. Thomas then worked at odd jobs in Kentucky and Tennessee before

22630-520: Was born on December 21, 1850, and died of a fever at the White House on February 20, 1862. The youngest, Thomas "Tad" Lincoln , was born on April 4, 1853, and survived his father, but died of heart failure at age 18 on July 16, 1871. Lincoln "was remarkably fond of children" and the Lincolns were not considered to be strict with their own. In fact, Lincoln's law partner William H. Herndon would grow irritated when Lincoln brought his children to

22785-597: Was due to George B. Dantzig , although much of the theory had been introduced by Leonid Kantorovich in 1939. ( Programming in this context does not refer to computer programming , but comes from the use of program by the United States military to refer to proposed training and logistics schedules, which were the problems Dantzig studied at that time.) Dantzig published the Simplex algorithm in 1947, and also John von Neumann and other researchers worked on

22940-516: Was due to increased incentive structures for mass education which in turn created a framework for the population to create and adapt new innovations and methods. Furthermore, the content of their education was composed of secular schooling that resulted in higher productivity levels and modern economic growth. Researchers at the Overseas Development Institute also highlight the importance of using economic growth to improve

23095-469: Was elected to the Illinois legislature, but before the term began in January he declined to take his seat so that he would be eligible to be a candidate in the upcoming U.S. Senate election. The year's elections showed the strong opposition to the Kansas–Nebraska Act, and in the aftermath Lincoln sought election to the U.S. Senate. At that time, senators were elected by state legislatures. After leading in

23250-529: Was going and replied, "To hell, I suppose". In 1844, the couple bought a house in Springfield near his law office. Mary kept house with the help of a hired servant and a relative. Lincoln was an affectionate husband and father of four sons, though his work regularly kept him away from home. The eldest, Robert Todd Lincoln , was born in 1843, and was the only child to live to maturity. Edward Baker Lincoln (Eddie), born in 1846, died February 1, 1850, probably of tuberculosis. Lincoln's third son, "Willie" Lincoln

23405-534: Was impossible without protectionism because import duties are necessary to shelter domestic " infant industries " until they could achieve economies of scale . Such theories proved influential in the United States, with much higher American average tariff rates on manufactured products between 1824 and the WWII period than most other countries, Nationalist policies, including protectionism, were pursued by American politician Henry Clay, and later by Abraham Lincoln , under

23560-434: Was lazy, for all his "reading—scribbling—writing—ciphering—writing poetry". His stepmother acknowledged he did not enjoy "physical labor" but loved to read. Lincoln was largely self-educated. His formal schooling was from itinerant teachers . It included two short stints in Kentucky, where he learned to read, but probably not to write. In Indiana at age seven, due to farm chores, he attended school only sporadically, for

23715-532: Was tall, strong, and athletic, and became adept at using an ax. He was an active wrestler during his youth and trained in the rough catch-as-catch-can style (also known as catch wrestling). He became county wrestling champion at the age of 21. He gained a reputation for his strength and audacity after winning a wrestling match with the renowned leader of ruffians known as the Clary's Grove boys. In March 1830, fearing another milk sickness outbreak, several members of

23870-540: Was the 16th president of the United States , serving from 1861 until his assassination in 1865. He led the United States through the American Civil War , defending the nation as a constitutional union , defeating the Confederacy , playing a major role in the abolition of slavery , expanding the power of the federal government , and modernizing the U.S. economy . Lincoln was born into poverty in

24025-435: Was the recipient of honorary degrees later in life, including an honorary Doctor of Laws from Columbia University in June 1861. When Lincoln was a teen, his "father grew more and more to depend on him for the 'farming, grubbing, hoeing, making fences' necessary to keep the family afloat. He also regularly hired his son out to work ... and by law, he was entitled to everything the boy earned until he came of age". Lincoln

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