Results 81 to 90 of about 241 (119)
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Even more with the Lemke complementarity algorithm
Mathematical Programming, 1986zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Alass of Complementary Cones and Lemke’s Algorithm
SIAM Journal on Applied Mathematics, 1972In this paper, a geometrical description of Lemke’s algorithm is presented for solving the linear complementarily problem: Find nonnegative vectors x and y satisfying $x = My + q$, $x^T y = 0$. This description is analogous to the simplicial description of the simplex method. A study is made of the class of all complementary cones and it is shown that,
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Extensions of Lemke's algorithm for the linear complementarity problem
Journal of Optimization Theory and Applications, 1976Lemke's algorithm for the linear complementarity problem fails when a desired pivot is not blocked. A projective transformation overcomes this difficulty. The transformation is performed computationally by adjoining a new row to a schema of the problem and pivoting on the element in this row and the unit constant column. Two new algorithms result; some
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Degeneracy Subgraph of the Lemke Complementary Pivot Algorithm and Anticycling Rule
Journal of Optimization Theory and Applications, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the average speed of Lemke's algorithm for quadratic programming
Mathematical Programming, 1986We show that the average number of steps of the Lemke algorithm for the quadratic programming problems grows at most linearly in the number of variables while fixing the number of constraints. The result and method were motivated by Smale's result on linear programming problems.
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A note on the Lemke-Howson algorithm
1974The Lemke-Howson algorithm for bimatrix games provides both an elementary proof of the existence of equilibrium points and an efficient computational method for finding at least one equilibrium point. The first half of this paper presents a geometrical view of the algorithm that makes its operation especially easy to visualize.
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On the Convergence of the Lemke–Howson Algorithm for Bi-Matrix Games
Journal of Mathematical Sciences, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On a Generalization of the Lemke–Howson Algorithm to Noncooperative N-Person Games
SIAM Journal on Applied Mathematics, 1971In [1] it has been shown that the existence of equilibrium points in a bimatrix game can be proved without a fixed-point theorem. If the game is nondegenerated, the number of equilibrium points is odd and all equilibrium points are obtained by a computational procedure in finitely many steps.The purpose of this note is to show that nondegeneracy can be
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On the Charnes-Lemke Algorithm for Linear Programming Problems with Multipage Structure
1992Numerous problems in areas such as transportation engineering, management decision making, and others can be formulated as large coupled linear programming problems. Subject to the coupling constraints that interrelate them, each linear programming problem can be viewed as a separate phase, or “page,” in a description of the overall model.
William M. Raike, John J. Rousseau
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The Ricardo-Lemke parametric algorithm on oddity and uniqueness [PDF]
, 2012 The parametric Lemke algorithm finds an odd number of solutions to the linear complementarity problem LCP (q, M), for a matrix M with zero blocks on the diagonal and vector q within a certain domain. A criterion for monotonicity and uniqueness is given.
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