This article is about the linear programming algorithm. For the non-linear optimization heuristic, see Nelder–Mead method.
In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.[1]
The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin.[2] 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.[3][4][5][6] 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.
^Murty, Katta G. (2000). Linear programming. John Wiley & Sons.
^Murty (1983, Comment 2.2)
^Murty (1983, Note 3.9)
^Stone, Richard E.; Tovey, Craig A. (1991). "The simplex and projective scaling algorithms as iteratively reweighted least squares methods". SIAM Review. 33 (2): 220–237. doi:10.1137/1033049. JSTOR 2031142. MR 1124362.
^Stone, Richard E.; Tovey, Craig A. (1991). "Erratum: The simplex and projective scaling algorithms as iteratively reweighted least squares methods". SIAM Review. 33 (3): 461. doi:10.1137/1033100. JSTOR 2031443. MR 1124362.
^Strang, Gilbert (1 June 1987). "Karmarkar's algorithm and its place in applied mathematics". The Mathematical Intelligencer. 9 (2): 4–10. doi:10.1007/BF03025891. ISSN 0343-6993. MR 0883185. S2CID 123541868.
optimization, Dantzig's simplexalgorithm (or simplex method) is a popular algorithm for linear programming. The name of the algorithm is derived from the...
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iterates need not converge). Simplexalgorithm of George Dantzig, designed for linear programming Extensions of the simplexalgorithm, designed for quadratic...
solution is integral. Consequently, the solution returned by the simplexalgorithm is guaranteed to be integral. To show that every basic feasible solution...
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solution quickly, and can then use branching towards the end. The simplexalgorithm is able to solve proper Sudokus, indicating if the Sudoku is not valid...
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programs, and developed a lexicographic simplexalgorithm. In contrast to the sequential algorithm, this simplexalgorithm considers all objective functions...
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optimal solutions. There are algorithms that can solve any problem in this category, such as the popular simplexalgorithm. Problems that can be solved...
tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead....
the linear program without the integer constraint using the regular simplexalgorithm. When an optimal solution is obtained, and this solution has a non-integer...
program using the simplexalgorithm is exponential, although the observed number of steps in practice is roughly linear. The simplexalgorithm is in fact much...
an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists...
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the problem is a linear programming problem. This can be solved by the simplex method, which usually works in polynomial time in the problem size but...
theoretical perspective: The standard algorithm for solving linear problems at the time was the simplexalgorithm, which has a run time that typically...
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