This report gives an overview of the linear complementarity problem, as a special case of mathematical programming with equilibrium constraints. The interior point method and two versions of Lemke’s method are reviewed, as methods for solving the linear complementarity problem. The report concludes with a description of the Stackelberg game and the bimatrix game as possible applications of math...

In this paper we consider the extended semide nite linear complementarity problem (XSDLCP). We propose merit functions that can constitute minimization problems equivalent to XSDLCP and show some properties of these functions. We also consider the semide nite nonlinear complementarity problem (SDNCP) and give new su cient conditions that guarantee the existence of a solution to SDNCP.

In this paper, we study some basic properties of the monotone semide nite nonlinear complementarity problem (SDCP). We show that the trajectory continuously accumulates into the solution set of the SDCP passing through the set of the infeasible but positive de nite matrices under certain conditions. Especially, for the monotone semide nite linear complementarity problem, the trajectory converge...

We consider a polyhedron intersected by a two-term disjunction, and we characterize the polyhedron resulting from taking its closed convex hull. This generalizes an earlier result of Conforti, Wolsey and Zambelli on split disjunctions. We also recover as a special case the valid inequalities derived by Judice, Sherali, Ribeiro and Faustino for linear complementarity problems.

We define a new fundamental constant associated with a P-matrix and show that this constant has various useful properties for the P-matrix linear complementarity problems (LCP). In particular, this constant is sharper than the Mathias-Pang constant in deriving perturbation bounds for the P-matrix LCP. Moreover, this new constant defines a measure of sensitivity of the solution of the P-matrix L...

New local and global error bounds are given for both nonmonotone and monotone linear complementarity problems. Comparisons of various residuals used in these error bounds are given. A possible candidate for a "best" error bound emerges from our comparisons as the sum of two natural residuals.

The paper establishes a computational encIosure of the solution of the linear complementarity problem (q, M), where M is assumed to be an H-matrix with a positive main diagonal. A dass of problems with interval data, which can arise in approximating the solutions of free boundary problems, is also treated successfully.

Although the general linear complementarity problem (LCP) is NP-complete, there are special classes that can be solved in polynomial time. One example is the type where the defining matrix is nondegenerate and for which the n-step property holds. In this paper we consider an extension of the property to the degenerate case by introducing the concept of an extended n-step vector and matrix. It i...

The linear complementarity problem (LCP) is one of the most widely studied mathematical programming problems. The theory of LCP can be extended to oriented matroids which are combinatorial abstractions of linear subspaces of Euclidean spaces. This paper briefly surveys the LCP, oriented matroids and algorithms for the LCP on oriented matroids. key words: linear complementarity problem, oriented...