Further Development in the Global Resolution of Convex Programs with Complementarity Constraints

Abstract

Abstract : Project Summary: This collaborative project aims at the study of the global resolution of convex programs with complementarity constraints (CPCCs), which form a large subclass of the class of mathematical programs with complementarity constraints (MPCCs). Despite the large literature on the local properties of an MPCC, there is a lack of systematic investigation on the computation of a globally optimal solution of these constrained optimization problems, or in the case where such a solution does not exist, on the generation of a certificate demonstrating the solution non-existence. While this is by no means an easy task, the pervasiveness of the CPCC in applications provides an important motivation for the undertaking of this project. Extending our previous study on the subclass of linear programs with linear complementarity constraints (LPCCs), which is essentially a linear program with additional complementarity constraints on certain pairs of variables, we have investigated the class of convex quadratic programs with complementarity constraints (QPCCs) and begun to explore the global resolution of the class of l0 optimization problems. Our work has provided a solid foundation for the design of efficient algorithms for obtaining a solution with provable quality of the class of highly challenging complementarity constrained optimization problems.