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79-398: Industrial technology programs typically include instruction in optimization theory , human factors , organizational behavior, industrial processes , industrial planning procedures, computer applications , and report and presentation preparation. Planning and designing manufacturing processes and equipment is the main aspect of being an industrial technologist. An industrial technologist

158-438: 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 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

237-783: A stock exchange , or in multiple other ways. Major stock exchanges include the Shanghai Stock Exchange , Singapore Exchange , Hong Kong Stock Exchange , New York Stock Exchange and NASDAQ (the US), the London Stock Exchange (UK), the Tokyo Stock Exchange (Japan), and Bombay Stock Exchange (India). Most countries with capital markets have at least one. Businesses that have gone public are subject to regulations concerning their internal governance, such as how executive officers' compensation

316-399: A "process optimization process". It is argued that BPM enables organizations to be more efficient, effective and capable of change than a functionally focused, traditional hierarchical management approach. Most legal jurisdictions specify the forms of ownership that a business can take, creating a body of commercial law applicable to business. The major factors affecting how a business

395-455: 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

474-479: A business. Some businesses are subject to ongoing special regulation, for example, public utilities , investment securities, banking, insurance, broadcasting , aviation , and health care providers. Environmental regulations are also very complex and can affect many businesses. When businesses need to raise money (called capital ), they sometimes offer securities for sale. Capital may be raised through private means, by an initial public offering or IPO on

553-422: 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

632-494: A certain technical area of study. Examples of this includes electronics , manufacturing , construction , graphics , automation / robotics , CADD , nanotechnology , aviation , etc. A major subject of study is technological development in industry. This has been defined as: Studies in this area often employ a multi-disciplinary research methodology and shade off into the wider analysis of business and economic growth (development, performance). The studies are often based on

711-498: A company-type management system. Many state institutions and enterprises in China and Russia have transformed into joint-stock companies, with part of their shares being listed on public stock markets. Business process management (BPM) is a holistic management approach focused on aligning all aspects of an organization with the wants and needs of clients . BPM attempts to improve processes continuously. It can, therefore, be described as

790-462: 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 the members of A have to satisfy. The domain A of f

869-451: A focus on practicality and management of technical systems with less focus on actual engineering of those systems. Typical curriculum at a four-year university might include courses on manufacturing process , technology and impact on society, mechanical and electronic systems, quality assurance and control , materials science , packaging , production and operations management , and manufacturing facility planning and design. In addition,

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948-480: 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. Business Business is the practice of making one's living or making money by producing or buying and selling products (such as goods and services ). It

1027-618: 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

1106-445: A mixture of industrial field research and desk-based data analysis and aim to be of interest and use to practitioners in business management and investment (etc.) as well as academics. In engineering , construction , textiles , food and drugs , chemicals and petroleum , and other industries, the focus has been on not only the nature and factors facilitating and hampering the introduction and utilization of new technologies but also

1185-524: A process known as an initial public offering (IPO) means that part of the business will be owned by members of the public. This requires the organization as a distinct entity, to disclose information to the public, and adhering to a tighter set of laws and procedures. Most public entities are corporations that have sold shares, but increasingly there are also public LLC's that sell units (sometimes also called shares), and other more exotic entities as well, such as, for example, real estate investment trusts in

1264-564: A range of human activity, from handicraft to high tech , but is most commonly applied to industrial production, in which raw materials are transformed into finished goods on a large scale. Marketing is defined by the American Marketing Association as "the activity, set of institutions, and processes for creating, communicating, delivering, and exchanging offerings that have value for customers, clients, partners, and society at large." The term developed from

1343-448: A share capital), this will be the shareholders . In a company limited by guarantee, this will be the guarantors. Some offshore jurisdictions have created special forms of offshore company in a bid to attract business for their jurisdictions. Examples include " segregated portfolio companies " and restricted purpose companies. There are, however, many, many sub-categories of types of company that can be formed in various jurisdictions in

1422-497: 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

1501-589: Is a field that deals with the study of money and investments . It includes the dynamics of assets and liabilities over time under conditions of different degrees of uncertainty and risk. In the context of business and management , finance deals with the problems of ensuring that the firm can safely and profitably carry out its operational and financial objectives; i.e. that it: (1) has sufficient cash flow for ongoing and upcoming operational expenses, and (2) can service both maturing short-term debt repayments, and scheduled long-term debt payments. Finance also deals with

1580-401: Is also "any activity or enterprise entered into for profit." A business entity is not necessarily separate from the owner and the creditors can hold the owner liable for debts the business has acquired. The taxation system for businesses is different from that of the corporates. A business structure does not allow for corporate tax rates. The proprietor is personally taxed on all income from

1659-845: Is also one of the largest industries used. "A career in industrial technology typically entails formal education from an accredited college or university. Opportunities are available to professionals with all levels of education. Those who hold associate degrees typically qualify for the entry-level technician and technologist positions, such as in the maintenance and operation of machinery. Bachelor's degree-holders could fill management and engineering positions, such as plant manager, production supervisor and quality systems engineering technologist. A graduate degree in industrial technology could qualify individuals for jobs in research, teaching and upper-level management". Industrial Technology includes wide-ranging subject matter and could be viewed as an amalgamation of industrial engineering and business topics with

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1738-587: Is an organization of workers who have come together to achieve common goals such as protecting the integrity of its trade, improving safety standards, achieving higher pay and benefits such as health care and retirement, increasing the number of employees an employer assigns to complete the work, and better working conditions . The trade union, through its leadership, bargains with the employer on behalf of union members ( rank and file members) and negotiates labor contracts ( collective bargaining ) with employers. The most common purpose of these associations or unions

1817-450: 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)

1896-419: Is crucial for all businesses to succeed as it helps companies adjust to a fast-moving business environment and the increasing demand for jobs. The term "Human Resource" was first coined by John R. Commons in his novel ' The Distribution of Wealth'. HR departments are relatively new as they began developing in the late 20th century. HR departments main goal is to maximize employee productivity and protecting

1975-455: 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

2054-648: Is determined, and when and how information is disclosed to shareholders and to the public. In the United States, these regulations are primarily implemented and enforced by the United States Securities and Exchange Commission (SEC). Other western nations have comparable regulatory bodies. The regulations are implemented and enforced by the China Securities Regulation Commission (CSRC) in China. In Singapore,

2133-566: Is for those who prefer an administrative role as it involves oversight of the entirety of the company. HRIS involves the storage and organization of employee data including full names, addresses, means of contact, and anything else required by that certain company. Some careers of those involved in the Human Resource field include enrollment specialists, HR analyst, recruiter, employment relations manager, etc. Many businesses have an Information technology (IT) department, which supports

2212-431: 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 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

2291-404: 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,

2370-509: 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

2449-461: 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

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2528-650: Is often responsible for implementing certain designs and processes. The USA-based Association of Technology, Management, and Applied Engineering (ATMAE), accredits selected collegiate programs in Industrial Technology in the USA. An instructor or graduate of an Industrial Technology program may choose to become a Certified Technology Manager (CTM) by sitting for a rigorous exam administered by ATMAE covering Production Planning & Control, Safety, Quality, and Management/Supervision. ATMAE program accreditation

2607-484: Is organized are usually: Many businesses are operated through a separate entity such as a corporation or a partnership (either formed with or without limited liability). Most legal jurisdictions allow people to organize such an entity by filing certain charter documents with the relevant Secretary of State or equivalent and complying with certain other ongoing obligations. The relationships and legal rights of shareholders , limited partners, or members are governed partly by

2686-481: Is recognized by the Council for Higher Education Accreditation (CHEA) for accrediting Industrial Technology programs. CHEA recognizes ATMAE in the U.S. for accrediting associate, baccalaureate, and master's degree programs in technology, applied technology, engineering technology, and technology-related disciplines delivered by national or regional accredited institutions in the United States.(2011) Industrial technology

2765-428: Is the process of exchanging goods and services. It is not just a single activity, but a set of activities that includes trade (buying and selling goods and services) and auxiliary services or aids to trade, that includes communication and marketing, logistics, finance, banking, insurance, and legal services related to trade. Business is also defined as engaging in commerce, as these are done in all businesses. Finance

2844-515: The long term objective of maximizing the value of the business, while also balancing risk and profitability; this includes the interrelated questions of (1) capital investment , which businesses and projects to invest in; (2) capital structure , deciding on the mix of funding to be used; and (3) dividend policy , what to do with "excess" capital. Human resources can be defined as division of business that involves finding, screening, recruiting , and training job applicants. Human resources, or HR,

2923-825: The " canary in the coal mine " and reduce the cost to businesses of protecting their employees. Sales are activity related to selling or the number of goods or services sold in a given time period. Sales are often integrated with all lines of business and are key to a companies' success. The efficient and effective operation of a business , and study of this subject, is called management . The major branches of management are financial management , marketing management, human resource management , strategic management , production management , operations management , service management , and information technology management . Owners may manage their businesses themselves, or employ managers to do so for them. Whether they are owners or employees, managers administer three primary components of

3002-595: 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

3081-475: The Industrial Technologist may have exposure to more vocational-style education in the form of courses on CNC manufacturing, welding , and other tools-of-the-trade in manufacturing. Industrial technology program graduates obtain a majority of positions which are applied engineering and/or management oriented. Since "industrial technologist" is not a common job title in the United States,

3160-475: The Internet, venture capital, bank loans, and debentures. Businesses often have important " intellectual property " that needs protection from competitors for the company to stay profitable. This could require patents , copyrights , trademarks , or preservation of trade secrets . Most businesses have names, logos, and similar branding techniques that could benefit from trademarking. Patents and copyrights in

3239-628: The Latin corpus , meaning body, and the Maurya Empire in Iron-Age India accorded legal rights to business entities. In many countries, it is difficult to compile all the laws that can affect a business into a single reference source. Laws can govern the treatment of labour and employee relations, worker protection and safety , discrimination on the basis of age, gender, disability, race, and in some jurisdictions, sexual orientation, and

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3318-650: The US, and unit trusts in the UK. A general partnership cannot "go public". A very detailed and well-established body of rules that evolved over a very long period of time applies to commercial transactions. The need to regulate trade and commerce and resolve business disputes helped shape the creation of law and courts. The Code of Hammurabi dates back to about 1772 BC for example and contains provisions that relate, among other matters, to shipping costs and dealings between merchants and brokers . The word "corporation" derives from

3397-689: The United States are largely governed by federal law, while trade secrets and trademarking are mostly a matter of state law. Because of the nature of intellectual property, a business needs protection in every jurisdiction in which they are concerned about competitors. Many countries are signatories to international treaties concerning intellectual property, and thus companies registered in these countries are subject to national laws bound by these treaties. In order to protect trade secrets, companies may require employees to sign noncompete clauses which will impose limitations on an employee's interactions with stakeholders, and competitors. A trade union (or labor union)

3476-541: The actual bachelor's degree or associate degree earned by the individual is obscured by the job title he/she receives. Typical job titles for industrial technologists having a bachelor's degree include quality systems engineer, manufacturing engineer, industrial engineer, plant manager, production supervisor, etc. Typical job titles for industrial technologists having a two-year associate degree include project technologist , manufacturing technologist, process technologist, etc. A technologist curriculum may focus or specialize in

3555-411: 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,

3634-408: 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"

3713-502: The business needs, an adviser can decide what kind is proprietorship will be most suitable. General partners in a partnership (other than a limited liability partnership), plus anyone who personally owns and operates a business without creating a separate legal entity, are personally liable for the debts and obligations of the business. Generally, corporations are required to pay tax just like "real" people. In some tax systems, this can give rise to so-called double taxation , because first

3792-455: The business's value: financial resources, capital (tangible resources), and human resources . These resources are administered in at least six functional areas: legal contracting, manufacturing or service production, marketing, accounting, financing, and human resources. In recent decades, states modeled some of their assets and enterprises after business enterprises. In 2003, for example, China modeled 80% of its state-owned enterprises on

3871-511: The business. A distinction is made in law and public offices between the term business and a company such as a corporation or cooperative . Colloquially, the terms are used interchangeably. Corporations are distinct from with sole proprietors and partnerships . They are separate legal entities and provide limited liability for their owners and members. They are subject to corporate tax rates. They are also more complicated and expensive to set up, but offer more protection and benefits for

3950-408: The charter documents and partly by the law of the jurisdiction where the entity is organized. Generally speaking, shareholders in a corporation, limited partners in a limited partnership, and members in a limited liability company are shielded from personal liability for the debts and obligations of the entity, which is legally treated as a separate "person". This means that unless there is misconduct,

4029-487: The company from any issues that may arise in the future. Some of the most common activities conducted by those working in HR include increasing innovation and creativity within a company, applying new approaches to work projects, and efficient training and communication with employees . Two of the most popular subdivisions of HR are Human Resource Management , HRM, and Human Resource Information Systems , or HRIS. The HRM route

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4108-512: 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

4187-579: The corporation pays tax on the profit, and then when the corporation distributes its profits to its owners, individuals have to include dividends in their income when they complete their personal tax returns, at which point a second layer of income tax is imposed. In most countries, there are laws that treat small corporations differently from large ones. They may be exempt from certain legal filing requirements or labor laws, have simplified procedures in specialized areas, and have simplified, advantageous, or slightly different tax treatment. "Going public" through

4266-403: 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

4345-671: The first stage of development of a potential new service or product. Research and development are very difficult to manage since the defining feature of the research is that the researchers do not know in advance exactly how to accomplish the desired result. Injuries cost businesses billions of dollars annually. Studies have shown how company acceptance and implementation of comprehensive safety and health management systems reduce incidents, insurance costs, and workers' compensation claims. New technologies, like wearable safety devices and available online safety training, continue to be developed to encourage employers to invest in protection beyond

4424-411: 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

4503-425: 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 the following is valid: it suffices to solve only minimization problems. However,

4582-425: 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

4661-473: The impact of new technologies on the production organization (etc.) of firms and various social and other wider aspects of the technological development process. How and When Technological development in industry Performed : Optimization theory 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

4740-566: The minimum wage, as well as unions , worker compensation, and working hours and leave. Some specialized businesses may also require licenses, either due to laws governing entry into certain trades, occupations or professions, that require special education or to raise revenue for local governments. Professions that require special licenses include law, medicine, piloting aircraft, selling liquor, radio broadcasting, selling investment securities, selling used cars, and roofing. Local jurisdictions may also require special licenses and taxes just to operate

4819-456: 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

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4898-406: 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

4977-401: 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 is always necessary to continuously evaluate the quality of

5056-488: The original meaning which referred literally to going to a market to buy or sell goods or services. Marketing tactics include advertising as well as determining product pricing . With the rise in technology, marketing is further divided into a class called digital marketing . It is marketing products and services using digital technologies. Research and development refer to activities in connection with corporate or government innovation. Research and development constitute

5135-399: The owner's own possessions are strongly protected in law if the business does not succeed. Where two or more individuals own a business together but have failed to organize a more specialized form of vehicle, they will be treated as a general partnership. The terms of a partnership are partly governed by a partnership agreement if one is created, and partly by the law of the jurisdiction where

5214-451: The owners and members. Forms of business ownership vary by jurisdiction , but several common entities exist: Less common types of companies are: "Ltd after the company's name signifies limited company, and PLC ( public limited company ) indicates that its shares are widely held." In legal parlance, the owners of a company are normally referred to as the "members". In a company limited or unlimited by shares (formed or incorporated with

5293-433: The partnership is located. No paperwork or filing is necessary to create a partnership, and without an agreement, the relationships and legal rights of the partners will be entirely governed by the law of the jurisdiction where the partnership is located. A single person who owns and runs a business is commonly known as a sole proprietor , whether that person owns it directly or through a formally organized entity. Depending on

5372-944: The regulatory authority is the Monetary Authority of Singapore (MAS), and in Hong Kong, it is the Securities and Futures Commission (SFC). The proliferation and increasing complexity of the laws governing business have forced increasing specialization in corporate law. It is not unheard of for certain kinds of corporate transactions to require a team of five to ten attorneys due to sprawling regulation. Commercial law spans general corporate law, employment and labor law , health-care law, securities law, mergers and acquisitions, tax law, employee benefit plans, food and drug regulation, intellectual property law on copyrights, patents, trademarks, telecommunications law, and financing. Other types of capital sourcing include crowdsourcing on

5451-420: The reputation of the exchange or particular market of exchange. Private companies do not have publicly traded shares, and often contain restrictions on transfers of shares. In some jurisdictions, private companies have maximum numbers of shareholders. A parent company is a company that owns enough voting stock in another firm to control management and operations by influencing or electing its board of directors;

5530-485: The second company being deemed as a subsidiary of the parent company. The subsidiary company can be allowed to maintain its own board of directors. The definition of a parent company differs by jurisdiction, with the definition normally being defined by way of laws dealing with companies in that jurisdiction. Accounting is the measurement, processing, and communication of financial information about economic entities such as businesses and corporations . The modern field

5609-419: 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

5688-509: 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

5767-405: 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

5846-422: 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

5925-494: The use of information technology and computer systems in support of enterprise goals. The role of a chief information officer is to lead this department. For example, Ford Motor Company in the United States employs "more than 3,000 team members with advanced computing, analytical and technical skills". Manufacturing is the production of merchandise for use or sale using labour and machines , tools , chemical and biological processing, or formulation. The term may refer to

6004-400: 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

6083-401: The world. Companies are also sometimes distinguished into public companies and private companies for legal and regulatory purposes. Public companies are companies whose shares can be publicly traded, often (although not always) on a stock exchange which imposes listing requirements / Listing Rules as to the issued shares, the trading of shares and a future issue of shares to help bolster

6162-597: 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

6241-515: Was established by the Italian mathematician Luca Pacioli in 1494. Accounting, which has been called the "language of business", measures the results of an organization's economic activities and conveys this information to a variety of users, including investors , creditors , management , and regulators . Practitioners of accounting are known as accountants . The terms "accounting" and "financial reporting" are often used as synonyms. Commerce

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