More on positive subdefinite matrices and the linear complementarity problem
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TLDR
In this article, the authors considered positive subdefinite matrices (PSBD) and showed that linear complementarity problems with PSBD matrices of rank ⩾ 2 are processable by Lemke's algorithm and that a PSBD matrix of rank 2 belongs to the class of sufficient matrices introduced by R.W. Cottle et al.About:
This article is published in Linear Algebra and its Applications.The article was published on 2001-11-15 and is currently open access. It has received 35 citations till now. The article focuses on the topics: Copositive matrix & Lemke's algorithm.read more
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Journal ArticleDOI
Some Properties of Generalized Positive Subdefinite Matrices
S. K. Neogy,A. K. Das +1 more
TL;DR: It is shown that for a subclass of GPSBD matrices, the solution set of a linear complementarity problem is same as the set of Karush--Kuhn--Tucker-stationary points of the corresponding quadratic programming problem.
Book ChapterDOI
On Generalized Positive Subdefinite Matrices and Interior Point Algorithm
TL;DR: This paper proposes an iterative and descent type interior point method to compute solution of linear complementarity problem LCP(q, A) given that A is real square matrix and q is a real vector and shows that the proposed algorithm converges to the solution of LCP(_, A), where A belongs to GPSBD class.
Journal ArticleDOI
On weak generalized positive subdefinite matrices and the linear complementarity problem
S. K. Neogy,A. K. Das +1 more
TL;DR: In this paper, a weaker version of the class of generalized positive subdefinite matrices introduced by Crouzeix and Komlosi is presented, which is new in the literature, and obtain some properties of weak generalized PSBD matrices.
Journal ArticleDOI
The Linear Complementarity Problem Under Asymptotic Analysis
Fabián Flores-Bazán,Rubén López +1 more
TL;DR: The present approach sheds new light on the classical linear complementarity problem LCP, and offers an alternative to view classical results.
Journal ArticleDOI
Characterizing Q-Matrices beyond L-Matrices
Fabián Flores-Bazán,Rubén López +1 more
TL;DR: In this article, the same result of Pang for a new class of matrices which properly contains class L was established for positive sub-definite matrices with rank one.
References
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Book
The Linear Complementarity Problem
TL;DR: In this article, the authors present an overview of existing and multiplicity of degree theory and propose pivoting methods and iterative methods for degree analysis, including sensitivity and stability analysis.
Journal ArticleDOI
Sufficient matrices and the linear complementarity problem
TL;DR: In this paper, the authors introduce the class of column sufficient matrices, which are the transpose of a matrix M such that for every vector q, the solutions of the linear complementarity problem are identical to the Karush-Kuhn-Tucker points associated with ( q, M ).
Journal ArticleDOI
Subdefinite Matrices and Quadratic Forms
TL;DR: In this paper, the authors define a new class of real symmetric matrices, which they call subdefinite, and investigate the properties of these matrices from a practical point of view.
Journal ArticleDOI
Affine pseudomonotone mappings and the linear complementarity problem
TL;DR: In this paper, it was shown that for affine pseudomonotone mapping, the feasibility of the (linear) complementarily problem implies its solvability, which was proved earlier by Karamardian under a strict feasibility condition.