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63-508: [REDACTED] Look up mip in Wiktionary, the free dictionary. MIP may refer to: Science [ edit ] Mixed integer programming , linear programming where some variables are constrained to be integers Minimum Ionizing Particle , in particle physics Maximum intensity projection , a computer visualization method Molecularly imprinted polymer , polymers processed using

126-712: A convex polytope over which the objective function is to be optimized. Linear programming can be applied to various fields of study. It is widely used in mathematics and, to a lesser extent, in business, economics , and some engineering problems. There is a close connection between linear programs, eigenequations, John von Neumann 's general equilibrium model, and structural equilibrium models (see dual linear program for details). Industries that use linear programming models include transportation, energy, telecommunications, and manufacturing. It has proven useful in modeling diverse types of problems in planning , routing , scheduling , assignment , and design. The problem of solving

189-527: A Luxembourgian political party in the 1960s Technology [ edit ] Male Iron Pipe, a plumbing pipe connection to an FIP (Female Iron Pipe); see National Pipe Thread Mega-frame Initialization Packet, an MPEG-2 Transport Stream packet used for synchronization in DVB-T single-frequency networks Memory in Pixel, a type of liquid crystal display Mipmap (multum in parvo, much in little space),

252-774: A TV and entertainment market museum in progress , a non-commercial art association, based in Vienna Most Improved Player (disambiguation) Business [ edit ] Mortgage insurance premium Managers in Partnership (MIP), a British trade union for healthcare managers Managing Intellectual Property , a monthly magazine specialized in intellectual property law and business Master in Ingegneria della Produzione (MIP), Politecnico di Milano School of Management Mint in Package;

315-480: A collectors' abbreviation; see Mint condition Government and politics [ edit ] Macroeconomic Imbalance Procedure , a European Union economic governance procedure Minor in Possession , in U.S. law, obtaining alcohol while under age Multilateral Interoperability Programme , a consortium of 29 NATO and Non-NATO nations Popular Independent Movement ( Mouvement indépendant populaire ),

378-407: A family of linear programming problems for which the simplex method takes a number of steps exponential in the problem size. In fact, for some time it was not known whether the linear programming problem was solvable in polynomial time , i.e. of complexity class P . Like the simplex algorithm of Dantzig, the criss-cross algorithm is a basis-exchange algorithm that pivots between bases. However,

441-428: A farmer has a piece of farm land, say L hectares , to be planted with either wheat or barley or some combination of the two. The farmer has F kilograms of fertilizer and P kilograms of pesticide. Every hectare of wheat requires F 1 kilograms of fertilizer and P 1 kilograms of pesticide, while every hectare of barley requires F 2 kilograms of fertilizer and P 2 kilograms of pesticide. Let S 1 be

504-497: A feasible solution at a vertex of the polytope and then walking along a path on the edges of the polytope to vertices with non-decreasing values of the objective function until an optimum is reached for sure. In many practical problems, " stalling " occurs: many pivots are made with no increase in the objective function. In rare practical problems, the usual versions of the simplex algorithm may actually "cycle". To avoid cycles, researchers developed new pivoting rules. In practice,

567-476: A meeting with John von Neumann to discuss his simplex method, von Neumann immediately conjectured the theory of duality by realizing that the problem he had been working in game theory was equivalent. Dantzig provided formal proof in an unpublished report "A Theorem on Linear Inequalities" on January 5, 1948. Dantzig's work was made available to public in 1951. In the post-war years, many industries applied it in their daily planning. Dantzig's original example

630-491: A point in the polytope where this function has the largest (or smallest) value if such a point exists. Linear programs are problems that can be expressed in standard form as Here the components of x {\displaystyle \mathbf {x} } are the variables to be determined, c {\displaystyle \mathbf {c} } and b {\displaystyle \mathbf {b} } are given vectors , and A {\displaystyle A}

693-482: A sequences of images, each of which is a progressively lower resolution than the previous Mobile IP , an IP protocol extension to provide mobility in the Internet See also [ edit ] MIPS (disambiguation) Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title MIP . If an internal link led you here, you may wish to change

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756-428: A severe form of multipath propagation . The radio receiver receives several echoes of the same signal, and the constructive or destructive interference among these echoes (also known as self-interference ) may result in fading . This is problematic especially in wideband communication and high-data rate digital communications, since the fading in that case is frequency-selective (as opposed to flat fading), and since

819-493: A system of linear inequalities dates back at least as far as Fourier , who in 1827 published a method for solving them, and after whom the method of Fourier–Motzkin elimination is named. In the late 1930s, Soviet mathematician Leonid Kantorovich and American economist Wassily Leontief independently delved into the practical applications of linear programming. Kantorovich focused on manufacturing schedules, while Leontief explored economic applications. Their groundbreaking work

882-459: Is a global maximum . An optimal solution need not exist, for two reasons. First, if the constraints are inconsistent, then no feasible solution exists: For instance, the constraints x  ≥ 2 and x  ≤ 1 cannot be satisfied jointly; in this case, we say that the LP is infeasible . Second, when the polytope is unbounded in the direction of the gradient of the objective function (where

945-504: Is a given matrix . The function whose value is to be maximized ( x ↦ c T x {\displaystyle \mathbf {x} \mapsto \mathbf {c} ^{\mathsf {T}}\mathbf {x} } in this case) is called the objective function . The constraints A x ≤ b {\displaystyle A\mathbf {x} \leq \mathbf {b} } and x ≥ 0 {\displaystyle \mathbf {x} \geq \mathbf {0} } specify

1008-399: Is a network planning aspect, in which the guard-interval is being separated into system time error and path time-error. A 100 ns step represents a 30 m difference, while 1 μs represents a 300 m difference. These distances needs to be compared with the worst-case distance between transmitter towers and reflections. Also, the time accuracy relates to nearby towers in a SFN domain, since a receiver

1071-447: Is a technique for the optimization of a linear objective function , subject to linear equality and linear inequality constraints . Its feasible region is a convex polytope , which is a set defined as the intersection of finitely many half spaces , each of which is defined by a linear inequality. Its objective function is a real -valued affine (linear) function defined on this polytope. A linear programming algorithm finds

1134-510: Is facilitated by the OFDM or COFDM modulation method. OFDM uses a large number of slow low-bandwidth modulators instead of one fast wide-band modulator. Each modulator has its own frequency sub-channel and sub-carrier frequency. Since each modulator is very slow, one can afford to insert a guard interval between the symbols, and thus eliminate the ISI. Although the fading is frequency-selective over

1197-539: Is not expected to see the signal from transmission towers being geographically far apart, so there is no accuracy requirements between these towers. So called GPS-free solutions exist, which essentially replace GPS as the timing distribution system. Such system may provide benefit in integration with transmission system for the MPEG-2 Transport Stream. It does not change any other aspect of the SFN system as

1260-422: Is primal feasible and that y  = ( y 1 ,  y 2 , ... ,  y m ) is dual feasible. Let ( w 1 ,  w 2 , ...,  w m ) denote the corresponding primal slack variables, and let ( z 1 ,  z 2 , ... ,  z n ) denote the corresponding dual slack variables. Then x and y are optimal for their respective problems if and only if So if

1323-458: Is slack in the dual (shadow) price non-negativity constraint requirement, i.e., the price is not zero, then there must be scarce supplies (no "leftovers"). Geometrically, the linear constraints define the feasible region , which is a convex polytope . A linear function is a convex function , which implies that every local minimum is a global minimum ; similarly, a linear function is a concave function , which implies that every local maximum

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1386-420: Is the fact that (for the symmetric dual) the dual of a dual linear program is the original primal linear program. Additionally, every feasible solution for a linear program gives a bound on the optimal value of the objective function of its dual. The weak duality theorem states that the objective function value of the dual at any feasible solution is always greater than or equal to the objective function value of

1449-417: Is the usual and most intuitive form of describing a linear programming problem. It consists of the following three parts: The problem is usually expressed in matrix form , and then becomes: Other forms, such as minimization problems, problems with constraints on alternative forms, and problems involving negative variables can always be rewritten into an equivalent problem in standard form. Suppose that

1512-560: The Philippines ) and in ATSC 3.0 . OFDM is also widely used in digital radio systems, including DAB , HD Radio , and T-DMB . Therefore, these systems are well-suited to SFN operation. In DVB-T a SFN functionality is described as a system in the implementation guide. It allows for re-transmitters, gap-filler transmitters (essentially a low-power synchronous transmitter) and use of SFN between main transmitter towers. The DVB-T SFN uses

1575-525: The dominating set problem are also covering LPs. Finding a fractional coloring of a graph is another example of a covering LP. In this case, there is one constraint for each vertex of the graph and one variable for each independent set of the graph. It is possible to obtain an optimal solution to the dual when only an optimal solution to the primal is known using the complementary slackness theorem. The theorem states: Suppose that x  = ( x 1 ,  x 2 , ... ,  x n )

1638-517: The i -th slack variable of the primal is not zero, then the i -th variable of the dual is equal to zero. Likewise, if the j -th slack variable of the dual is not zero, then the j -th variable of the primal is equal to zero. This necessary condition for optimality conveys a fairly simple economic principle. In standard form (when maximizing), if there is slack in a constrained primal resource (i.e., there are "leftovers"), then additional quantities of that resource must have no value. Likewise, if there

1701-432: The minimum principle for concave functions ) since linear functions are both convex and concave. However, some problems have distinct optimal solutions; for example, the problem of finding a feasible solution to a system of linear inequalities is a linear programming problem in which the objective function is the zero function (i.e., the constant function taking the value zero everywhere). For this feasibility problem with

1764-531: The LP feasible region, there exists a set of d (or fewer) inequality constraints from the LP such that, when we treat those d constraints as equalities, the unique solution is x . Thereby we can study these vertices by means of looking at certain subsets of the set of all constraints (a discrete set), rather than the continuum of LP solutions. This principle underlies the simplex algorithm for solving linear programs. The simplex algorithm , developed by George Dantzig in 1947, solves LP problems by constructing

1827-505: The MPEG-2 Transport Stream forming a mega-frame. The MIP is time-stamped in the SFN adapter, as measured relative the PPS signal and counted in 100 ns steps (period time of 10 MHz) with the maximum delay (programmed into the SFN adapter) alongside. The SYNC adapter measures the MIP packet against its local variant of PPS using the 10 MHz to measure the actual network delay and then withholding

1890-444: The SFN results in ghosting due to echoes of the same signal. A simplified form of SFN can be achieved by a low power co-channel repeater , booster or broadcast translator , which is utilized as a gap filler transmitter. The aim of SFNs is efficient utilization of the radio spectrum , allowing a higher number of radio and TV programs in comparison to traditional multi-frequency network (MFN) transmission. An SFN may also increase

1953-400: The amount of unused pesticide. In matrix form this becomes: Every linear programming problem, referred to as a primal problem, can be converted into a dual problem , which provides an upper bound to the optimal value of the primal problem. In matrix form, we can express the primal problem as: An alternative primal formulation is: There are two ideas fundamental to duality theory. One

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2016-631: The basic requirements can be met. While not designed with on-channel repeaters in mind, the 8VSB modulation method used in North America for digital TV is relatively good at ghost cancellation . Early experiments at WPSU-TV led to an ATSC standard for SFNs, A/110. ATSC SFNs have seen widest use in mountainous areas like Puerto Rico and Southern California , but are also in use or planned in gentler terrain. Early ATSC tuners were not very good at handling multipath propagation, but later systems have seen significant improvements. Through

2079-574: The central concepts of optimization theory, such as duality, decomposition, and the importance of convexity and its generalizations. Likewise, linear programming was heavily used in the early formation of microeconomics , and it is currently utilized in company management, such as planning, production, transportation, and technology. Although the modern management issues are ever-changing, most companies would like to maximize profits and minimize costs with limited resources. Google also uses linear programming to stabilize YouTube videos. Standard form

2142-404: The common form of the simplex algorithm . This form introduces non-negative slack variables to replace inequalities with equalities in the constraints. The problems can then be written in the following block matrix form: where s {\displaystyle \mathbf {s} } are the newly introduced slack variables, x {\displaystyle \mathbf {x} } are

2205-489: The coverage area and decrease the outage probability in comparison to an MFN, since the total received signal strength may increase to positions midway between the transmitters. SFN schemes are somewhat analogous to what in non- broadcast wireless communication, for example cellular networks and wireless computer networks, is called transmitter macrodiversity , CDMA soft handoff and Dynamic Single Frequency Networks (DSFN). SFN transmission can be considered as creating

2268-489: The criss-cross algorithm need not maintain feasibility, but can pivot rather from a feasible basis to an infeasible basis. The criss-cross algorithm does not have polynomial time-complexity for linear programming. Both algorithms visit all 2 corners of a (perturbed) cube in dimension  D , the Klee–Minty cube , in the worst case . In contrast to the simplex algorithm, which finds an optimal solution by traversing

2331-422: The decision variables, and z {\displaystyle z} is the variable to be maximized. The example above is converted into the following augmented form: where x 3 , x 4 , x 5 {\displaystyle x_{3},x_{4},x_{5}} are (non-negative) slack variables, representing in this example the unused area, the amount of unused fertilizer, and

2394-490: The edges between vertices on a polyhedral set, interior-point methods move through the interior of the feasible region. This is the first worst-case polynomial-time algorithm ever found for linear programming. To solve a problem which has n variables and can be encoded in L input bits, this algorithm runs in O ( n 6 L ) {\displaystyle O(n^{6}L)} time. Leonid Khachiyan solved this long-standing complexity issue in 1979 with

2457-562: The fact that the guard interval of the COFDM signal allows for various length of path echoes to occur is not different from that of multiple transmitters transmitting the same signal onto the same frequency. The critical parameters is that it needs to occur about in the same time and at the same frequency. The versatility of time-transfer systems such as GPS receivers (here assumed to provide PPS and 10 MHz signals) as well as other similar systems allows for phase and frequency coordination among

2520-461: The gradient of the objective function is the vector of the coefficients of the objective function), then no optimal value is attained because it is always possible to do better than any finite value of the objective function. Otherwise, if a feasible solution exists and if the constraint set is bounded, then the optimum value is always attained on the boundary of the constraint set, by the maximum principle for convex functions (alternatively, by

2583-407: The introduction of the ellipsoid method . The convergence analysis has (real-number) predecessors, notably the iterative methods developed by Naum Z. Shor and the approximation algorithms by Arkadi Nemirovski and D. Yudin. Khachiyan's algorithm was of landmark importance for establishing the polynomial-time solvability of linear programs. The algorithm was not a computational break-through, as

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2646-568: The later simplex method . Hitchcock had died in 1957, and the Nobel Memorial Prize is not awarded posthumously. From 1946 to 1947 George B. Dantzig independently developed general linear programming formulation to use for planning problems in the US Air Force. In 1947, Dantzig also invented the simplex method that, for the first time efficiently, tackled the linear programming problem in most cases. When Dantzig arranged

2709-450: The link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=MIP&oldid=1229384745 " Category : Disambiguation pages Hidden categories: Articles containing French-language text Short description is different from Wikidata All article disambiguation pages All disambiguation pages Mixed integer programming More formally, linear programming

2772-440: The maximum inspiratory pressure is the highest atmospheric pressure developed during inspiration against an occluded airway Methylation induced premeiotically Mid-inguinal point Molecular Inversion Probe Mitochondrial intermediate peptidase , an enzyme MIP (gene) , a gene in humans Microprotein , a small protein encoded from small open reading frames Arts and entertainment [ edit ] Mipcom ,

2835-585: The molecular imprinting technique with affinity to a chosen 'template molecule' Moon Impact Probe , of the Indian lunar satellite Chandrayaan-1 Model Intercomparison Project; see Coupled model intercomparison project MIP, an interactive proof system complexity class; see Interactive proof system Mars ISPP Precursor, a test payload intended to be flown on the cancelled Mars Surveyor 2001 Lander Biology [ edit ] Macrophage inflammatory protein , in biology Maximum Inspiratory Pressure ,

2898-925: The number of possible solutions that must be checked. The linear programming problem was first shown to be solvable in polynomial time by Leonid Khachiyan in 1979, but a larger theoretical and practical breakthrough in the field came in 1984 when Narendra Karmarkar introduced a new interior-point method for solving linear-programming problems. Linear programming is a widely used field of optimization for several reasons. Many practical problems in operations research can be expressed as linear programming problems. Certain special cases of linear programming, such as network flow problems and multicommodity flow problems , are considered important enough to have much research on specialized algorithms. A number of algorithms for other types of optimization problems work by solving linear programming problems as sub-problems. Historically, ideas from linear programming have inspired many of

2961-516: The packets until the maximum delay is achieved. The details is to be found in ETSI TR 101 190 and mega-frame details in ETSI TS 101 191. It should be understood that the resolution of the mega-frame format is being in steps of 100 ns, whereas the accuracy needs can be in the range of 1-5 μs. The resolution is sufficient for the needed accuracy. There is no strict need for an accuracy limit as this

3024-405: The primal at any feasible solution. The strong duality theorem states that if the primal has an optimal solution, x , then the dual also has an optimal solution, y , and c x = b y . A linear program can also be unbounded or infeasible. Duality theory tells us that if the primal is unbounded then the dual is infeasible by the weak duality theorem. Likewise, if the dual is unbounded, then

3087-403: The primal must be infeasible. However, it is possible for both the dual and the primal to be infeasible. See dual linear program for details and several more examples. A covering LP is a linear program of the form: such that the matrix A and the vectors b and c are non-negative. The dual of a covering LP is a packing LP , a linear program of the form: such that the matrix A and

3150-483: The selling price of wheat and S 2 be the selling price of barley, per hectare. If we denote the area of land planted with wheat and barley by x 1 and x 2 respectively, then profit can be maximized by choosing optimal values for x 1 and x 2 . This problem can be expressed with the following linear programming problem in the standard form: In matrix form this becomes: Linear programming problems can be converted into an augmented form in order to apply

3213-403: The simplex algorithm is quite efficient and can be guaranteed to find the global optimum if certain precautions against cycling are taken. The simplex algorithm has been proved to solve "random" problems efficiently, i.e. in a cubic number of steps, which is similar to its behavior on practical problems. However, the simplex algorithm has poor worst-case behavior: Klee and Minty constructed

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3276-480: The simplex method is more efficient for all but specially constructed families of linear programs. However, Khachiyan's algorithm inspired new lines of research in linear programming. In 1984, N. Karmarkar proposed a projective method for linear programming. Karmarkar's algorithm improved on Khachiyan's worst-case polynomial bound (giving O ( n 3.5 L ) {\displaystyle O(n^{3.5}L)} ). Karmarkar claimed that his algorithm

3339-440: The time spreading of the echoes may result in intersymbol interference (ISI). Fading and ISI can be avoided by means of diversity schemes and equalization filters . Transmitters, which are part of a SFN, should not be used for navigation via direction finding as the direction of signal minima or signal maxima can differ from the direction to the transmitter. In wideband digital broadcasting , self-interference cancellation

3402-416: The transmitters. The guard interval allows for a timing budget, of which several microseconds may be allocated to time errors of the time-transfer system used. A GPS receiver worst-case scenario is able to provide +/- 1 μs time, well within the system needs of DVB-T SFN in typical configuration. In order to achieve the same transmission time on all transmitters, the transmission delay in the network providing

3465-504: The transport to the transmitters needs to be considered. Since the delay from the originating site to the transmitter varies, a system is needed to add delay on the output side such that the signal reaches the transmitters at the same time. This is achieved by the use of special information inserted into the data stream called the Mega-frame Initialization Packet (MIP) which is inserted using a special marker in

3528-426: The vectors b and c are non-negative. Covering and packing LPs commonly arise as a linear programming relaxation of a combinatorial problem and are important in the study of approximation algorithms . For example, the LP relaxations of the set packing problem , the independent set problem , and the matching problem are packing LPs. The LP relaxations of the set cover problem , the vertex cover problem , and

3591-438: The wartime successes propelled linear programming into the spotlight. Post-WWII, the method gained widespread recognition and became a cornerstone in various fields, from operations research to economics. The overlooked contributions of Kantorovich and Leontief in the late 1930s eventually became foundational to the broader acceptance and utilization of linear programming in optimizing decision-making processes. Kantorovich's work

3654-550: The whole frequency channel, it can be considered as flat within the narrowband sub-channel. Thus, advanced equalization filters can be avoided. A forward error correction code (FEC) can counteract some of the sub-carriers being exposed to too much fading to be correctly demodulated. OFDM is utilized in the terrestrial digital TV broadcasting system DVB-T (used in Europe and other regions), ISDB-T (used in Japan , Brazil , and

3717-423: The zero-function for its objective-function, if there are two distinct solutions, then every convex combination of the solutions is a solution. The vertices of the polytope are also called basic feasible solutions . The reason for this choice of name is as follows. Let d denote the number of variables. Then the fundamental theorem of linear inequalities implies (for feasible problems) that for every vertex x of

3780-584: Was initially neglected in the USSR . About the same time as Kantorovich, the Dutch-American economist T. C. Koopmans formulated classical economic problems as linear programs. Kantorovich and Koopmans later shared the 1975 Nobel Memorial Prize in Economic Sciences . In 1941, Frank Lauren Hitchcock also formulated transportation problems as linear programs and gave a solution very similar to

3843-447: Was largely overlooked for decades. The turning point came during World War II when linear programming emerged as a vital tool. It found extensive use in addressing complex wartime challenges, including transportation logistics, scheduling, and resource allocation. Linear programming proved invaluable in optimizing these processes while considering critical constraints such as costs and resource availability. Despite its initial obscurity,

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3906-602: Was much faster in practical LP than the simplex method, a claim that created great interest in interior-point methods. Since Karmarkar's discovery, many interior-point methods have been proposed and analyzed. Single-frequency network A single-frequency network or SFN is a broadcast network where several transmitters simultaneously send the same signal over the same frequency channel. Analog AM and FM radio broadcast networks as well as digital broadcast networks can operate in this manner. SFNs are not generally compatible with analog television transmission, since

3969-453: Was to find the best assignment of 70 people to 70 jobs. The computing power required to test all the permutations to select the best assignment is vast; the number of possible configurations exceeds the number of particles in the observable universe . However, it takes only a moment to find the optimum solution by posing the problem as a linear program and applying the simplex algorithm . The theory behind linear programming drastically reduces

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