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

TL;DR

This paper introduces a MATLAB implementation combining regularization and SQP methods to solve MPCC problems, addressing the challenge of constraint qualification failure by iterative approximation techniques.

Contribution

It develops a novel algorithm integrating regularization and SQP with dual iterative processes to effectively solve MPCCs.

Findings

Algorithms successfully solved MPCC test problems

Performance comparison shows competitive efficiency

Method handles constraint qualification issues effectively

Abstract

Mathematical Program with Complementarity Constraints (MPCC) plays a very important role in many fields such as engineering design, economic equilibrium, multilevel game, 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 Mangasarian-Fromovitz 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 try 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 \cite{MacMPEC} were tested. The algorithms performance comparative analysis was carried out.