Results 231 to 240 of about 105,781 (281)

A Linear Complementarity Problem with a P-Matrix

SIAM Review, 2004
Summary: We present an application of a linear complementarity problem where \(M\) is a P-matrix but, in general, is neither an H-matrix nor a positive definite matrix. This application occurs originally by \textit{J. Rohn} [Linear Algebra Appl. 126, 39--78 (1989; Zbl 0712.65029)], which is less known to the LCP community. Its focus is in computing the
Uwe Schäfer
exaly   +2 more sources

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.
M Seetharama Gowda, Roman Sznajder
exaly   +3 more sources

On Solution Stability of the Linear Complementarity Problem

Mathematics of Operations Research, 1992
In the paper [5], C. D Ha introduced the notion of stability of a linear complementarity problem at a solution point and established several sufficient conditions for stability to hold. In the present paper, we derive some new stability results which significantly improve Ha's results.
M Seetharama Gowda, Jong-Shi Pang
exaly   +3 more sources

Generalized linear complementarity problems

Mathematical Programming, 1990
The 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.
M. Seetharama Gowda, Thomas I. Seidman
openaire   +2 more sources

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 ...
M. Seetharama Gowda, Yoon J. Song
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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.
Jonathan M. Borwein, M. A. H. Dempster
openaire   +1 more source

On the Linear Complementarity Problem

Management Science, 1975
Consider 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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The Linear Complementarity Problem

Management Science, 1971
This study centers on the task of efficiently finding a solution of the linear complementarity problem: Ix − My = q, x ≥ 0, y ≥ 0, x ⊥ y. The main results are: (1) It is shown that Lemke's algorithm will solve (or show no solution exists) the problem for M ∈ L where L is a class of matrices, which properly includes (i) certain copositive matrices, (ii)
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Generalized Linear Complementarity Problems

Mathematics of Operations Research, 1995
We 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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