Two characterization theorems in complementarity theory
type: Item
instance of: scholarly article
title: Two characterization theorems in complementarity theory
zbMATH Open document ID: 0643.90087
DOI: 10.1016/0167-6377(88)90048-X
published in: Operations Research Letters
publication date: 1988-01-01T00:00:00Z
review text: Two main results are proved in this paper. The first theorem concerns the linear complementarity problem (LCP) \(w=q+Mx\geq 0\), \(x\geq 0\), \(w^ Tx=0\) where q is a given n-vector and M is a given \(n\times n\) metric. It is shown that M is non-degenerate \(\Leftrightarrow\) For each vector q, the problem has a finite number of solutions \(\Leftrightarrow\) For each vector q, each solution to the problem is locally unique. The second theorem concerns the differentiability of a solution to the parametric nonlinear complementarity problem (NCP): \(w=f(x,\lambda)\geq 0\), \(x\geq 0\) and \(w^ Tx=0\) where \(f: R^ n\times R^ m\to R^ n\). A necessary and sufficient condition for x(\(\lambda)\) to be differentiable is stated and proved where x(\(\lambda)\) is a solution of (NCP) for a given \(\lambda \in R^ m\).
reviewed by: R. N. Kaul
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 4049418
zbMATH Keywords: linear complementarity
zbMATH Keywords: locally unique
zbMATH Keywords: differentiability of a solution
zbMATH Keywords: parametric nonlinear complementarity
author: Jong-Shi Pang
MaRDI profile type: Publication
cites work: Uniqueness and differentiability of solutions of parametric nonlinear complementarity problems
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cites work: Lipschitz Continuity of Solutions of Linear Inequalities, Programs and Complementarity Problems
cites work: On the parametric nonlinear complementarity problem
cites work: Q4039868
cites work: On the number of solutions to the complementarity problem and spanning properties of complementary cones
cites work: Strongly Regular Generalized Equations
cites work: Sensitivity analysis for variational inequalities
full work available at URL: 0167-6377(88)90048-x
OpenAlex ID: W2048287854
description: scientific article; zbMATH DE number 4049418