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On the Equivalence of Linear Complementarity Problems [PDF]
Operations Research Letters, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alberto Bemporad +2 more
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Generalized Linear Complementarity Problems
Mathematics of Operations Research, 1995We introduce the concept of the generalized (monotone) linear complementarity problem (GLCP) in order to unify LP, convex QP, monotone LCP, and mixed monotone LCP. We establish the basic properties of GLCP and develop canonical forms for its representation. We show that the GLCP reduces to a monotone LCP in the same variables.
Osman Güler
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The Linear Order Complementarity Problem
Mathematics of Operations Research, 1989The classical complementarity problem in Euclidean space can be viewed alternatively as a variational inequality or as a lattice orthogonality problem. Generalizations of the former have been extensively studied, but infinite-dimensional analogues of the latter have been largely ignored.
Jonathan M. Borwein, M. A. H. Dempster
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Generalized linear complementarity problems
Mathematical Programming, 1990The generalization is twofold. First, the problem is defined for closed convex cones rather than for the non-negative orthant. Second, some, but not all, the results are stated for infinite-dimensional real Hilbert spaces. Two infinite-dimensional existence results are given.
M. Seetharama Gowda, Thomas I. Seidman
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On semidefinite linear complementarity problems
Mathematical Programming, 2000The paper deals with the SemiDefinite Linear Complementarity Problem (SDLCP\((L,S^n_+)\): find a matrix \(X \in S^n_+\) such that \(Y=L(x)+Q \in S^n_+\) and and \(\langle X,Y\rangle=0\), where \(S^n\) (\(S^n_+\)) denote the set of symmetric (positive semidefinite) matrices, \(L: S^n \rightarrow S^n\) is a linear transformation, \(Q \in S^n\) and ...
M. Seetharama Gowda, Yoon J. Song
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On the Linear Complementarity Problem
Management Science, 1975Consider the linear complementarity problem given in the system: [Formula: see text] where, W, Z and q are vectors of dimension n. M is a matrix of order n × n and ZT is the transpose of Z. Any (Z, W) satisfying (1), (2), and (3) is a complementary feasible solution to system (I).
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Linearized Methods for Tensor Complementarity Problems
Journal of Optimization Theory and Applications, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hong-Bo Guan, Dong-Hui Li
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The Linear Complementarity Problem
Management Science, 1971This study centers on the task of efficiently finding a solution of the linear complementarity problem: Ix − My = q, x ≥ 0, y ≥ 0, x ⊥ y. The main results are: (1) It is shown that Lemke's algorithm will solve (or show no solution exists) the problem for M ∈ L where L is a class of matrices, which properly includes (i) certain copositive matrices, (ii)
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Sparse Linear Complementarity Problems
2013In this paper, we study the sparse linear complementarity problem, denoted by k-LCP: the coefficient matrix has at most k nonzero entries per row. It is known that 1-LCP is solvable in linear time, while 3-LCP is strongly NP-hard. We show that 2-LCP is strongly NP-hard, while it can be solved in O(n 3 logn) time if it is sign-balanced, i.e., each row ...
Hanna Sumita +2 more
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On Solution Stability of the Linear Complementarity Problem
Mathematics of Operations Research, 1992In the paper [5], C. D Ha introduced the notion of stability of a linear complementarity problem at a solution point and established several sufficient conditions for stability to hold. In the present paper, we derive some new stability results which significantly improve Ha's results.
M. Seetharama Gowda, Jong-Shi Pang
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