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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.
Gowda, M. Seetharama, Seidman, Thomas I.
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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.
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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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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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Continuous linear complementarity problem
Journal of Optimization Theory and Applications, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Anderson, E. J., Aramendia, M.
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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
Cunningham, William H., Geelen, James F.
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Stochastic $R_0$ Matrix Linear Complementarity Problems
SIAM Journal on Optimization, 2007The authors consider the expected residual minimization method (ERM) for solving stochastic linear complementarity problems \[ x \geq 0 , ~~ M(\omega) x + q(\omega) \geq 0, ~~ x^T(M(\omega) x + q(\omega)) = 0 . \] This problem is transformed to a minimization problem \(\min G(x) \text{ s.t. } x \geq 0\). The study is based on the concept of stochastic \
Fang, Haitao +2 more
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SOLVING STRONGLY MONOTONE LINEAR COMPLEMENTARITY PROBLEMS
International Game Theory Review, 2013Given a linear transformation L on a finite dimensional real inner product space V to itself and an element q ∈ V we consider the general linear complementarity problem LCP (L, K, q) on a proper cone K ⊆ V. We observe that the iterates generated by any closed algorithmic map will converge to a solution for LCP (L, K, q), whenever L is strongly monotone.
A. CHANDRASHEKARAN +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.
Gowda, M. Seetharama, Sznajder, Roman
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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.
Chandrasekaran, R. +2 more
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