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.

Linear complementarity problem (LCP) is studied. After reforming general LCP as the system of nonlinear equations by NCP-function, equivalent to solving an unconstrained optimization model, which can be solved a recently proposed algorithm named novel global harmony search (NGHS). NGHS overcome disadvantage interior-point methods. Numerical results show that has higher rate convergence than oth...

T paper shows how many types of combinatorial problems can be embedded in continuous space and solved as nonconvex optimization problems. If the objective function and the constraints are linear, problems of this kind can be formulated as linear complementarity problems. An algorithm is presented to solve this type of problem and indicate its convergence properties. Computational comparisons ar...

A simple and uniied analysis is provided on the rate of local convergence for a class of high-order-infeasible-path-following algorithms for the P-linear complementarity problem (P-LCP). It is shown that the rate of local convergence of a-order algorithm with a centering step is + 1 if there is a strictly complementary solution and (+ 1)=2 otherwise. For the-order algorithm without the centerin...