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Linear complementarity, linear and nonlinear programming
01 Jan 1988-
About: The article was published on 1988-01-01 and is currently open access. It has received 1012 citations till now. The article focuses on the topics: Mixed complementarity problem & Complementarity theory.
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TL;DR: An algorithm to compute the minimum norm solution of the positive semidefinite linear complementarity problem is presented and its solution can be obtained using the alternative theorems and a convenient characterization of the solution set of a convex quadratic programming problem.
Abstract: In this article, we present an algorithm to compute the minimum norm solution of the positive semidefinite linear complementarity problem. We show that its solution can be obtained using the alternative theorems and a convenient characterization of the solution set of a convex quadratic programming problem. This problem reduces to an unconstrained minimization problem with once differentiable convex objective function. We propose an extension of Newton's method for solving the unconstrained optimization problem. Computational results show that convergence to high accuracy often occurs in just a few iterations.
16 citations
01 Jan 2006
TL;DR: In this article, strongly polynomial algorithms for solving linear programsmin(Sigma x_i |S ) with constraints S of the monotonic discounted form x ≥ λx_j + β with 0 < λ < 1.
Abstract: We suggest new strongly polynomial algorithms for solving linear programsmin( \Sigma x_i |S ) with constraints S of the monotonic discounted form x_i ≥ λx_j + β with 0 < λ < 1. The algorithm ...
16 citations
TL;DR: In this paper, the convergence conditions of the modulus-based matrix splitting iteration method for nonlinear complementarity problem of H-matrices are weakened and the convergence domain given by the proposed theorems is larger than the existing ones.
Abstract: In this paper, the convergence conditions of the modulus-based matrix splitting iteration method for nonlinear complementarity problem of H-matrices are weakened. The convergence domain given by the proposed theorems is larger than the existing ones. Numerical examples show the advantages of the new theorems.
16 citations
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TL;DR: In this paper, some useful necessary and sufficient conditions for the unique solution of the generalized absolute value equation (GAVE) are presented and some new sufficient conditions are obtained, which are weaker than the previous published works.
Abstract: In this paper, some useful necessary and sufficient conditions for the unique solution of the generalized absolute value equation (GAVE) $Ax-B|x|=b$ with $A, B\in \mathbb{R}^{n\times n}$ from the optimization field are first presented, which cover the fundamental theorem for the unique solution of the linear system $Ax=b$ with $A\in \mathbb{R}^{n\times n}$. Not only that, some new sufficient conditions for the unique solution of the GAVE are obtained, which are weaker than the previous published works.
16 citations
TL;DR: An efficient Block-LCP method is proposed that reduces an LCP with big size to a sequence of sub-LCPs with mild size which can be solved by a variety of LCP solvers and the best solver is identified through numerical experiments and Convergence of Markov chain approximation is proved.
16 citations