An RLT Approach for Solving the Binary-Constrained Mixed Linear Complementarity Problem

Abstract

It is well known that the mixed linear complementarity problem can be used to model equilibria in energy markets as well as a host of other engineeringand economic problems. The binary-constrained mixed linear complementarity problem is a formulation of the mixed linear complementarity problemin which some variables are restricted to be binary. This paper presents anovel approach for solving the binary-constrained mixed linear complementarityproblem. First we solve a series of linear optimization problems that enablesus to replace some of the complementarity constraints with linear equations.Then we solve an equivalent mixed integer linear programming formulation ofthe original binary-constrained mixed linear complementarity problem (witha smaller number of complementarity constraints) to guarantee a solution tothe problem. Our computational results on a wide range of test problems,including some engineering examples, demonstrate the usefulness and the effectiveness of this novel approach