Title
Charactarizations of Linear Suboptimality for Mathematical Programs with Equilibrium Constraints
Document Type
Technical Report
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 modern variational analysis and applications. In contrast to standard notions, it admits complete characterizations 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.
Number in Series
2006.07
Disciplines
Applied Mathematics | Mathematics
AMS Subject Classification
90C30, 49J52, 49J53
Recommended Citation
Mordukhovich, Boris S., "Charactarizations of Linear Suboptimality for Mathematical Programs with Equilibrium Constraints" (2006). Mathematics Research Reports. 37.
https://digitalcommons.wayne.edu/math_reports/37
Comments
Dedicated to Boris Polyak in honor of his 70th birthday. Research was partially supported by the National Science Foundation under grant DMS-0304989 and by the Australian Research Council under grant DP-0451168.