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Bland's Rule
In mathematical optimization, Bland's rule (also known as Bland's algorithm, Bland's anti-cycling rule or Bland's pivot rule) is an algorithmic refinement of the simplex method for linear optimization. With Bland's rule, the simplex algorithm solves feasible linear optimization problems without cycling.. The original simplex algorithm starts with an arbitrary basic feasible solution, and then changes the basis in order to decrease the minimization target and find an optimal solution. Usually, the target indeed decreases in every step, and thus after a bounded number of steps an optimal solution is found. However, there are examples of degenerate linear programs, on which the original simplex algorithm cycles forever. It gets stuck at a basic feasible solution (a corner of the feasible polytope) and changes bases in a cyclic way without decreasing the minimization target. Such cycles are avoided by Bland's rule for choosing a column to enter and a column to leave the basis. Bland ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts 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 maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jack Edmonds
Jack R. Edmonds (born April 5, 1934) is an American-born and educated computer scientist and mathematician who lived and worked in Canada for much of his life. He has made fundamental contributions to the fields of combinatorial optimization, polyhedral combinatorics, discrete mathematics and the theory of computing. He was the recipient of the 1985 John von Neumann Theory Prize. Early career Edmonds attended Duke University before completing his undergraduate degree at George Washington University in 1957. He thereafter received a master's degree in 1960 at the University of Maryland under Bruce L. Reinhart with a thesis on the problem of embedding graphs into surfaces. From 1959 to 1969 he worked at the National Institute of Standards and Technology (then the National Bureau of Standards), and was a founding member of Alan J. Goldman, Alan Goldman’s newly created Operations Research Section in 1961. Goldman proved to be a crucial influence by enabling Edmonds to work in a RAND ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization Algorithms And Methods
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts 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 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. More generally, optimization includes finding "best available" values of some objective function given a define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Schrijver
Alexander (Lex) Schrijver (born 4 May 1948 in Amsterdam) is a Dutch mathematician and computer scientist, a professor of discrete mathematics and optimization at the University of Amsterdam and a fellow at the Centrum Wiskunde & Informatica in Amsterdam.Profile CWI, retrieved 2012-03-30. Since 1993 he has been co-editor in chief of the journal ''''.''Combinatorica'' journal home page Springer, retrieved 2012-03-30. Biography Schrijver earned his Ph.D. in 1977 from the |
Christos H
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Christos may refer to: * Jesus of Nazareth * Christ (title), a title for the Jewish Messiah in Christianity * Christos (surname) * Christos (given name) *, a Greek owned, Liberian flagged cargo ship in service 1962-71 See also * Christ (other) * Christo (other) * Christa (other) * Christus (other) Christus may refer to: * Christ (title) People * Petrus Christus (c. 1410s – c. 1475), Dutch painter * Sir Christus (1978–2017), Finnish musician Music * ''Christus'' (Liszt), an oratorio * ''Christus'' (Mendelssohn), an unfinished orator ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albert W
Albert may refer to: Companies * Albert (supermarket), a supermarket chain in the Czech Republic * Albert Heijn, a supermarket chain in the Netherlands * Albert Market, a street market in The Gambia * Albert Productions, a record label * Albert Computers, Inc., a computer manufacturer in the 1980s Entertainment * ''Albert'' (1985 film), a Czechoslovak film directed by František Vláčil * ''Albert'' (2015 film), a film by Karsten Kiilerich * ''Albert'' (2016 film), an American TV movie * ''Albert'' (Ed Hall album), 1988 * "Albert" (short story), by Leo Tolstoy * Albert (comics), a character in Marvel Comics * Albert (''Discworld''), a character in Terry Pratchett's ''Discworld'' series * Albert, a character in Dario Argento's 1977 film ''Suspiria'' Military * Battle of Albert (1914), a WWI battle at Albert, Somme, France * Battle of Albert (1916), a WWI battle at Albert, Somme, France * Battle of Albert (1918), a WWI battle at Albert, Somme, France People * Albert (given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George B
George may refer to: People * George (given name) * George (surname) * George (singer), American-Canadian singer George Nozuka, known by the mononym George * George Washington, First President of the United States * George W. Bush, 43rd President of the United States * George H. W. Bush, 41st President of the United States * George V, King of Great Britain, Ireland, the British Dominions and Emperor of India from 1910-1936 * George VI, King of Great Britain, Ireland, the British Dominions and Emperor of India from 1936-1952 * Prince George of Wales * George Papagheorghe also known as Jorge / GEØRGE * George, stage name of Giorgio Moroder * George Harrison, an English musician and singer-songwriter Places South Africa * George, Western Cape ** George Airport United States * George, Iowa * George, Missouri * George, Washington * George County, Mississippi * George Air Force Base, a former U.S. Air Force base located in California Characters * George (Peppa Pig), a 2-year-old pig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Criss-cross Algorithm
In mathematical optimization, the criss-cross algorithm is any of a family of algorithms for linear programming. Variants of the criss-cross algorithm also solve more general problems with linear inequality constraints and nonlinear objective functions; there are criss-cross algorithms for linear-fractional programming problems, quadratic-programming problems, and linear complementarity problems. Like the simplex algorithm of George B. Dantzig, the criss-cross algorithm is not a polynomial-time algorithm for linear programming. Both algorithms visit all 2''D'' corners of a (perturbed) cube in dimension ''D'', the Klee–Minty cube (after Victor Klee and George J. Minty), in the worst case. However, when it is started at a random corner, the criss-cross algorithm on average visits only ''D'' additional corners.The simplex algorithm takes on average ''D'' steps for a cube. : Thus, for the three-dimensional cube, the algorithm visits all 8 c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oriented Matroid
An oriented matroid is a mathematics, mathematical mathematical structure, structure that abstracts the properties of directed graphs, Vector space, vector arrangements over ordered fields, and Arrangement of hyperplanes, hyperplane arrangements over ordered fields. In comparison, an ordinary (i.e., non-oriented) matroid abstracts the linear independence, dependence properties that are common both to Graph (discrete mathematics), graphs, which are not necessarily ''directed'', and to arrangements of vectors over field (mathematics), fields, which are not necessarily ''ordered''. All oriented matroids have an underlying matroid. Thus, results on ordinary matroids can be applied to oriented matroids. However, the conversion (logic), converse is false; some matroids cannot become an oriented matroid by ''orienting'' an underlying structure (e.g., circuits or independent sets). The distinction between matroids and oriented matroids is discussed further below. Matroids are often usefu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simplex Method
In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming. The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. Simplices are not actually used in the method, but one interpretation of it is that it operates on simplicial ''cones'', and these become proper simplices with an additional constraint. The simplicial cones in question are the corners (i.e., the neighborhoods of the vertices) of a geometric object called a polytope. The shape of this polytope is defined by the constraints applied to the objective function. History George Dantzig worked on planning methods for the US Army Air Force during World War II using a desk calculator. During 1946 his colleague challenged him to mechanize the planning process to distract him from taking another job. Dantzig formulated the problem as linear inequalities inspired by the work of Wassily Leontief, however, at that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Center For Operations Research And Econometrics
The Center for Operations Research and Econometrics (CORE) is an interdisciplinary research institute of the University of Louvain (UCLouvain) located in Louvain-la-Neuve, Belgium. Since 2010, it is part of the Louvain Institute of Data Analysis and Modeling in economics and statistics (LIDAM), along with the Institute for Economic and Social Research (IRES), Louvain Finance (LFIN) and the Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA). CORE integrates fundamental and applied research in the following key fields: economics and game theory, econometrics, quantitative and economic geography, and operations research. Researchers at CORE aim at developing a theoretical and methodological base for the analysis of decision problems related to economic policy and the management of the public and private sector, the theory of optimisation and statistics for the solution of design and decision problems, and computational tools (algorithms and software). Histo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cornell University
Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach and make contributions in all fields of knowledge—from the classics to the sciences, and from the theoretical to the applied. These ideals, unconventional for the time, are captured in Cornell's founding principle, a popular 1868 quotation from founder Ezra Cornell: "I would found an institution where any person can find instruction in any study." Cornell is ranked among the top global universities. The university is organized into seven undergraduate colleges and seven graduate divisions at its main Ithaca campus, with each college and division defining its specific admission standards and academic programs in near autonomy. The university also administers three satellite campuses, two in New York City and one in Education City, Qatar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
