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Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming 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 ...
Dantzig–Wolfe decomposition is an algorithm for solving linear programming problems with special structure. It was originally developed by George Dantzig and Philip Wolfe and initially published in 1960. [1] Many texts on linear programming have sections dedicated to discussing this decomposition algorithm. [2][3][4][5][6][7] Dantzig–Wolfe ...
Simplex algorithm. 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 ...
The assignment problem consists of finding, in a weighted bipartite graph, a matching of a given size, in which the sum of weights of the edges is minimum. If the numbers of agents and tasks are equal, then the problem is called balanced assignment. Otherwise, it is called unbalanced assignment. [1] If the total cost of the assignment for all ...
Linear complementarity problem. In mathematical optimization theory, the linear complementarity problem (LCP) arises frequently in computational mechanics and encompasses the well-known quadratic programming as a special case. It was proposed by Cottle and Dantzig in 1968. [1][2][3]
Revised simplex method. In mathematical optimization, the revised simplex method is a variant of George Dantzig 's simplex method for linear programming. The revised simplex method is mathematically equivalent to the standard simplex method but differs in implementation. Instead of maintaining a tableau which explicitly represents the ...
The following problem classes are all convex optimization problems, or can be reduced to convex optimization problems via simple transformations: [7]: chpt.4 [10] A hierarchy of convex optimization problems. (LP: linear programming, QP: quadratic programming, SOCP second-order cone program, SDP: semidefinite programming, CP: conic optimization.)
Big M method. In operations research, the Big M method is a method of solving linear programming problems using the simplex algorithm. The Big M method extends the simplex algorithm to problems that contain "greater-than" constraints. It does so by associating the constraints with large negative constants which would not be part of any optimal ...