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

I. Figueiredo, J. Júdice and S. Rosa

Abstract

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 plate with a rigid obstacle. This MPEC can be reduced to a nonlinear programming problem with independent variables implicitely defined by the solution of a mixed linear complementarity problem (MLCP). 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 metodology in practice.