We consider the linear complementarity problem (LCP): Mz + q ≥ 0, z ≥ 0, z′(Mz + q) = 0 as an absolute value equation (AVE): (M + I)z + q = |(M − I)z + q|, where M is an n× n square matrix and I is the identity matrix. We propose a concave minimization algorithm for solving (AVE) that consists of solving a few linear programs, typically two. The algorithm was tested on 500 consecutively generat...

The first algorithm to use a complementary pivoting procedure was that devised by Lemke and Howson to find a Nash equilibrium point of a bimatrix game [ 15 ]. This algorithm introduced a novel proof of convergence not relying on standard monotonicity arguments. Lemke [ 12] generalized his complementary pivot algorithm to solve certain classes of linear complementarity problem (LCP), which Dantz...

The globally uniquely solvable (GUS) property of the linear transformation of the linear complementarity problems over symmetric cones has been studied recently by Gowda et al. via the approach of Euclidean Jordan algebra. In this paper, we contribute a new approach to characterizing the GUS property of the linear transformation of the second-order cone linear complementarity problems (SOCLCP) ...

Optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximal complementary solutions. Maximal complementary solutions can be characterized by optimal (tri)partitions. On the other hand, the solutions provided by simplex{based pivot algorithms are given in terms of complementary bases. A basis identi cation algorithm is a...

We introduce a new matrix class Pc, which consists of those matrices M for which the solution set of the corresponding linear complementarity problem is connected for every q 2 I R n. We consider Lemke's pivotal method from the perspective of piecewise linear homotopies and normal maps and show that Lemke's method processes all matrices in Pc \Q0. We further investigate the relationship of the ...

A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-No part of this Journal may be reproduced in any form, by print, photoprint, microolm or any other means without written permission from Abstract In this paper we show that the primal{dual Dikin aane scaling algorithm for linear programming of Jansen, Roos and Terlaky enhances an asymptotical O(p nL) com...

This paper presents an approach to solving discretely constrained, mixed linear complementarity problems (DC-MLCPs). Such formulations include a variety of interesting and realistic models of which two are highlighted: a market-clearing auction typical in electric power markets but suitable in other more general contexts, and a network equilibrium suitable to energy markets as well as other gri...

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 if M is rank-symmetric and principally uni...

In this paper, we discuss a polynomial and Q-subquadratically convergent algorithm for linear complementarity problems that does not require feasibility of the initial point or the subsequent iterates. The algorithm is a modiication of the linearly convergent method of Zhang and requires the solution of at most two linear systems with the same coeecient matrix at each iteration.