Convergence of optimal values of quadratic penalty problems for mathematical programs with complementarity constraints

Abstract

In this note, a mathematical program with complementarity constraints (MPCC) is reformulated as a nonsmooth constrained mathematical program via the Fischer-Burmeister function. Quadratic penalty functions are used to treat this nonsmooth constrained program. We investigate necessary and sufficient conditions that guarantee the convergence of optimal values of unconstrained penalized problems to the optimal value of the original MPCC.