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...

Techniques for transforming convex quadratic programs (QPs) into monotone linear complementarity problems (LCPs) and vice versa are well known. We describe a class of LCPs for which a reduced QP formulation|one that has fewer constraints than the \stan-dard" QP formulation|is available. We mention several instances of this class, including the known case in which the coeecient matrix in the LCP...

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...

This paper investigates the Lipschitz continuity of the solution map in the settings of horizontal, vertical, and mixed linear complementarity problems. In each of these cases, we show that the solution map is (globally) Lipschitzian if and only if the solution map is single-valued. These generalize a similar result of Murthy, Parthasarathy, and Sabatini proved in the LCP setting.

This paper presents a stochastic equilibrium model for deregulated natural gas markets. Each market participant (pipeline operators, producers, etc.) solves a stochastic optimization problem whose optimality conditions, when combined with market-clearing conditions give rise to a certain mixed complementarity problem (MiCP). The stochastic aspects are depicted by a recourse problem for each pla...

In this paper, we extended the result about the error estimation for linear complementarity problem to the extended linear complementarity problem (ELCP) in management equilibrium modeling. More precisely, we first present that the level set of a computable residual function is bounded, and give error estimation in level set. Based on this, we use this residual function to establish a global er...