A globally convergent sequential linear programming algorithm for mathematical programs with linear complementarity constraints

This paper presents a sequential linear programming algorithm for computing a stationary point of a mathematical program with linear equilibrium constraints. The algorithm is based on a formulation of equilibrium constraints as a system of semi smooth equations by means of a perturbed Fischer-Burmeister functional. Using only data of the problem, we introduce a new method to update the parameter that characterizes the aforesaid perturbed functional. With the aim of avoiding the need to choose penalty parameters, we introduce a simple restoration step. Some computational results are reported.