Partially B-Regular optimization and equilibrium problems

• 成果类型: Article
• 署名作者: Pang, J. S.
• 署名单位: Rensselaer Polytechnic Institute
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1070.0262
• 发表日期: 2007
• 页码: 687-699
• 关键词: mathematical programs; optimality conditions; constraint qualifications; relaxation algorithms; GLOBAL CONVERGENCE; Nash equilibria; electric-power; stationarity; systems

摘要

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.