Combining the regularization strategy and the SQP to solve MPCC - A MATLAB implementation

Abstract

Mathematical Program with Complementarity Constraints (MPCC) plays a very important role in many fields such as engineering design, economic equilibrium, multilevel games, and mathematical programming theory itself. In theory its constraints fail to satisfy a standard constraint qualification such as the linear independence constraint qualification (LICQ) or the MangasarianFromovitz constraint qualification (MFCQ) at any feasible point. As a result, the developed nonlinear programming theory may not be applied to MPCC class directly. Nowadays, a natural and popular approach is trying to find some suitable approximations of an MPCC so that it can be solved by solving a sequence of nonlinear programs. This work aims to solve the MPCC using nonlinear programming techniques, namely the SQP and the regularization scheme. Some algorithms with two iterative processes, the inner and the external, were developed. A set of AMPL problems from MacMPEC database (Leyffer, 2000) [8] were tested. The comparative analysis regarding performance of algorithms was carried out. © 2010 Elsevier B.V. All rights reserved.