A smooth QP-free algorithm without a penalty function or a filter for mathematical programs with complementarity constraints

Abstract

In this paper, a smooth QP-free algorithm without a penalty function or a filter is proposed for a special kind of mathematical programs with complementarity constraints (MPCC for short). Firstly, the investigated problem is transformed into sequential parametric standard nonlinear programs by perturbed techniques and a generalized complementarity function. Then the trial step, at each iteration, is accepted such that either the value of the objective function or the measure of the constraint violation is sufficiently reduced. Finally, it is shown that every limit point of the iterative sequence is feasible, and there exists a limit point that is a KKT point for the problem under mild conditions.