A class of mathematical programs with equilibrium constraints: A smooth algorithm and applications to contact problems

We discuss a special mathematical programming problem with equilibrium constraints (MPEC), that arises in material and shape optimization problems involving the contact of a rod or a plate with a rigid obstacle. This MPEC can be reduced to a nonlinear programming problem with independent variables and some dependent variables implicitly defined by the solution of a mixed linear complementarity problem. A projected-gradient algorithm including a complementarity method is proposed to solve this optimization problem. Several numerical examples are reported to illustrate the efficiency of this methodology in practice.