Partially B-Regular Optimization and Equilibrium Problems

This paper introduces a concept termed partial B–regularity for a feasible solution to a bivariate constraint system and shows that this condition leads to the equivalence between the B–stationarity of a pair of lifted and unlifted programs. In particular, for an optimization problem with a univariate pseudoconvex objective function constrained by such a nonconvex bivariate system, partial B–regularity provides a sufficient condition for a B–stationary point to be globally optimal. Applications of partial B–regularity to several classes of optimization and equilibrium problems are presented; these include a lexicographic optimization problem, a nonconvex mathematical program with equilibrium constraints (MPEC) that arises from a convex implicit value–function optimization problem, and a Nash equilibrium program with equilibrium constraints.