A penalty function approach for mathematical programs with variational inequality constraints

The problem of solving a mathematical programme with variational inequality or nonlinear complementarity constraints arises quite frequently in the analysis of physical and socio-economic systems. The current state-of-the-art for solving such problems is heuristic. This paper presents an exterior-point penalty method based on M.J. Smith’s optimization formulation of the finite-dimensional variational inequality problem and the simplicial decomposition algorithm for this problem class. Numerical results are presented to illustrate the potential of this technique for solving problems of realistic size.