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...

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...

In this paper we deene the Extended Linear Complementarity Problem (ELCP), an extension of the well-known Linear Complementarity Problem (LCP). We study the general solution set of an ELCP and we present an algorithm to nd all its solutions. Finally we show that the ELCP can be used to solve some important problems in the max algebra.

In this paper we deene the Extended Linear Complementarity Problem (ELCP), an extension of the well-known Linear Complementarity Problem (LCP). We show that the ELCP can be viewed as a kind of unifying framework for the LCP and its various generalizations. We study the general solution set of an ELCP and we develop an algorithm to nd all its solutions. We also show that the general ELCP is an N...

We show that the problem of finding optimal strategies for both players in a simple stochastic game reduces to the generalized linear complementarity problem (GLCP) with a P-matrix, a well-studied problem whose hardness would imply NP = co-NP. This makes the rich GLCP theory and numerous existing algorithms available for simple stochastic games. As a special case, we get a reduction from binary...

In this paper we study a rst-order and a high-order algorithm for solving linear complementarity problems. These algorithms are implicitly associated with a large neighborhood whose size may depend on the dimension of the problems. The complexity of these algorithms depends on the size of the neighborhood. For the rst order algorithm, we achieve the complexity bound which the typical large-step...