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Integral Solutions of Linear Complementarity Problems
Mathematics of Operations Research, 1998We characterize the class of integral square matrices M having the property that for every integral vector q the linear complementarity problem with data M, q has only integral basic solutions. These matrices, called principally unimodular matrices, are those for which every principal nonsingular submatrix is unimodular. As a consequence, we show that
William H. Cunningham, James F. Geelen
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Integer Solution for Linear Complementarity Problem
Mathematics of Operations Research, 1998We consider the problem of finding an integer solution to a linear complementarity problem. We introduce the class I of matrices for which the corresponding linear complementarity problem has an integer complementary solution for every vector, q, for which it has a solution.
R. Chandrasekaran +2 more
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On the Solution Sets of Linear Complementarity Problems
SIAM Journal on Matrix Analysis and Applications, 2000The authors consider two problems related to the solution sets of linear complementarity problems of the following form \[ Az+ q\geq 0,\quad z\geq 0\quad\text{and}\quad z^t(Az+ q)= 0. \] For this problems, the connectedness and convexity of the solution sets is studied.
G. S. R. Murthy +2 more
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The Generalized Order Linear Complementarity Problem
SIAM Journal on Matrix Analysis and Applications, 1994Summary: The generalized order linear complementarity problem (in the setting of a finite-dimensional vector lattice) is the problem of finding a solution to the piecewise-linear system \[ x\wedge (M_1 x+ q_1)\wedge (M_2 x+ q_2)\wedge\cdots\wedge (M_k x+ q_k)= 0, \] where \(M_i\)'s are linear transformations and \(q_i\)'s are vectors.
M. Seetharama Gowda, Roman Sznajder
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Cycling in linear complementarity problems
Mathematical Programming, 1979A bound for the minimum length of a cycle in Lemke's Algorithm is derived. An example illustrates that this bound is sharp, and that the fewest number of variables is seven.
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Complementarity problems in linear complementarity systems
Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207), 1998Complementarity systems are described by differential and algebraic equations and inequalities similar to those appearing in the linear complementarity problem (LCP) of mathematical programming. Typical examples of such systems include mechanical systems subject to unilateral constraints, electrical networks with diodes, processes subject to relays and/
Heemels, W.P.M.H. +2 more
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Linear complementarity problems and bi-linear games
Applications of Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sengodan, Gokulraj +1 more
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On the Parametric Linear Complementarity Problem
Journal of Optimization Theory and Applications, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Degeneracy in linear complementarity problems: a survey
Annals of Operations Research, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Linear Complementarity Problem with a P-Matrix
SIAM Review, 2004Summary: We present an application of a linear complementarity problem where \(M\) is a P-matrix but, in general, is neither an H-matrix nor a positive definite matrix. This application occurs originally by \textit{J. Rohn} [Linear Algebra Appl. 126, 39--78 (1989; Zbl 0712.65029)], which is less known to the LCP community. Its focus is in computing the
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