CHARACTERIZATIONS OF LINEAR SUBOPTIMALITY FOR MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS1

Abstract

Dedicated to Boris Polyak in honor of his 70th birthday Abstract. The paper is devoted to the study of a new notion of linear suboptimality in constrained mathematical programming. This concept is different from conventional notions of solutions to optimization-related problems, while seems to be natural and significant from the viewpoint of mod-ern variational analysis and applications. In contrast to standard notions, it admits complete char-acterizations via appropriate constructions of generalized differentiation in nonconvex settings. In this paper we mainly focus on various classes of mathematical programs with equilibrium constraints {MPECs), whose principal role has been well recognized in optimization theory and its applications. Based on robust generalized differential calculus, we derive new results giving pointwise necessary and sufficient conditions for linear suboptimality in general MPECs and its important specifications involving variational and quasi variational inequalities, implicit complementarity problems, etc. Key words. nonsmooth optimization-variational analysis-generalized differentiation-mathematica