Convergence of a local regularization approach for mathematical programmes with complementarity or vanishing constraints

Mathematical programs with equilibrium or vanishing constraints (MPECs or MPVCs) are both known to be difficult optimization problems which typically violate all standard constraint qualifications. A number of methods try to exploit the particular structure of MPECs and MPVCs in order to overcome these difficulties. In a recent paper by Ulbrich and Veelken [37], this was done for MPECs by a local regularization idea that may be viewed as a modification of the popular global regularization technique by Scholtes [33]. The aim of this paper is twofold: First, we improve the convergence theory from [37] in the MPEC setting, and second we translate this local regularization idea to MPVCs and obtain a new solution method for this class of optimization problems for which several convergence results are given.