Variational analysis and full stability of optimal solutions to constrained and minimax problems. (July 2015)

• Record Type: Journal Article
• Authors: Mordukhovich, Boris S.; Sarabi, M. Ebrahim
• Is Part Of: Nonlinear analysis. Volume 121(2015)
• Page Start: 36
• Page End: 53
• Publication Date: 2015-07
• Subjects: Variational analysis -- Constrained parametric optimization -- Full stability of local minimizers -- Strong regularity -- Second-order subdifferentials -- Graphical derivative -- Minimax problem; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2014.10.013
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The main goal of this paper is to develop applications of advanced tools of first-order and second-order variational analysis and generalized differentiation to the fundamental notion of full stability of local minimizers of general classes of constrained optimization and minimax problems. In particular, we derive second-order characterizations of full stability and investigate its relationships with other notions of stability for parameterized conic programs and minimax problems. Furthermore, the developed variational approach allows us to largely unify and provide new self-contained proofs of some quite recent results in this direction for problems of constrained optimization with C 2 -smooth data.