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.

The paper generalizes the Mangasarian-Ren 10] error bounds for linear complementarity problems (LCPs) to nonlinear complementarity problems (NCPs). This is done by extending the concept of R 0-matrix to several R 0-type functions, which include a subset of monotone functions as a special case. Both local and global error bounds are obtained for the R 0-type and some monotone NCPs.

We study the problem of solving a constrained system of nonlinear equations by a combination of the classical damped Newton method for (unconstrained) smooth equations and the recent interior point potential reduction methods for linear programs, linear and nonlin-ear complementarity problems. In general, constrained equations provide a uniied formulation for many mathematical programming probl...

It has been shown by Lemke that if a matrix is copositive plus on IR n , then feasibility of the corresponding Linear Complementarity Problem implies solvability. In this article we show, under suitable conditions, that feasibility of a Generalized Linear Complementarity Problem (i.e., deened over a more general closed convex cone in a real Hilbert Space) implies solvability whenever the operat...

A Mathematical Program with Linear Complementarity Constraints (MPLCC) is an optimization problem where a continuously differentiable function is minimized on a set defined by linear constraints and complementarity conditions on pairs of complementary variables. This problem finds many applications in several areas of science, engineering and economics and is also an important tool for the solu...

We propose a homogeneous model for the class of mixed horizontal linear complementarity problems. The proposed homogeneous model is always solvable and provides the solution of the original problem if it exists, or a certificate of infeasibility otherwise. Our formulation preserves the sparsity of the original formulation and does not reduce to the homogeneous model of the equivalent standard l...

A new algorithm for the solution of large-scale nonlinear complementarity problems is introduced. The algorithm is based on a nonsmooth equation reformulation of the complementarity problem and on an inexact Levenberg-Marquardt-type algorithm for its solution. Under mild assumptions, and requiring only the approximate solution of a linear system at each iteration, the algorithm is shown to be b...

Variational inequality theory besides being elegant, exciting and rich, also provides us a unified and natural framework to study a large class of linear and nonlinear problems arising in mathematical and engineering sciences. Equally important is the area of operations research known as complementarity theory, which has received much attention during the last twenty years. It has been shown by...