Penalty Type Methods for Mathematical Programs with Complementarity Constraints^{1}

X. Q. Yang and X. X. Huang

Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China.

Abstract. In this paper, a mathematical program with complementarity constraints (MPCC) is reformulated as a nonsmooth constrained optimization problem by using the Fischer-Burmeister function. Penalty type methods are applied to transform the resulted constrained optimization problem into unconstrained optimization problems. Some of these penalty functions may not be locally Lipschitz. Using an approximate smooth variational principle, we derive optimality conditions for unconstrained optimization problems of (MPCC) and establish that the limit point of a sequence of points that satisfy the second-order necessary optimality conditions of unconstrained optimization problems is a strongly stationary point of the original (MPCC) under some conditions.

Keywords: Mathematical program with complementarity constraints, nonlinear penalty function, optimality condition, B-stationary point.

1This research is supported by the Research Grants Council of Hong Kong (PolyU B-Q359.)