Results 231 to 240 of about 91,873 (257)

Integral Solutions of Linear Complementarity Problems

Mathematics of Operations Research, 1998
We 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, 2007
The 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, Chen, Xiaojun, Fukushima, Masao   +2 more
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SOLVING STRONGLY MONOTONE LINEAR COMPLEMENTARITY PROBLEMS

International Game Theory Review, 2013
Given 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, T. PARTHASARATHY, V. VETRIVEL   +2 more
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The Generalized Order Linear Complementarity Problem

SIAM Journal on Matrix Analysis and Applications, 1994
Summary: 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, 1998
We 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., Kabadi, S. N., Sridhar, R.   +2 more
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Sparse Linear Complementarity Problems

2013
In 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, Naonori Kakimura, Kazuhisa Makino   +2 more
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Γ-robust linear complementarity problems

Optimization Methods and Software, 2020
Complementarity problems are often used to compute equilibria made up of specifically coordinated solutions of different optimization problems.
Vanessa Krebs, Martin Schmidt
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Equivalence of the Generalized Vertical Block Linear Complementarity Problems and Linear Complementarity Problems

Mediterranean Journal of Mathematics, 2005
In this paper, generalization of a vertical block linear complementarity problem associated with two different types of matrices, one of which is a square matrix and the other is a vertical block matrix, is proposed. The necessary and sufficient conditions for the existence of the solution of the generalized vertical block linear complementarity ...
Bidushi Chakraborty, Sudarshan Nanda, Mahendra Prasad Biswal   +2 more
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The Linear Order Complementarity Problem

Mathematics of Operations Research, 1989
The 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.
J. M. Borwein, M. A. H. Dempster
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On semidefinite linear complementarity problems

Mathematical Programming, 2000
The 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 ...
Gowda, M. Seetharama, Song, Yoon
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