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Partially B-Regular Optimization and Equilibrium Problems

Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180
pangj{at}rpi.edu

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.

Key Words: partial B-regularity; equilibrium constraints; stationary points; lexicographic optimization
History: Received: January 29, 2006; revision received: October 5, 2006;