Hölder weak sharp minimizers and Hölder tilt-stability. (June 2015)

• Record Type: Journal Article
• Authors: Zheng, Xi Yin; Ng, Kung-Fu
• Is Part Of: Nonlinear analysis. Volume 120(2015)
• Page Start: 186
• Page End: 201
• Publication Date: 2015-06
• Subjects: 90C31 -- 49K40 -- 49J52; Hölder weak sharp minimizer -- Stable Hölder weak sharp minimizer -- Hölder tilt-stable minimizer -- Hölder metric regularity; 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.2015.02.020
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we introduce and study the notions of Hölder weak sharp minimizers, stable Hölder weak sharp minimizers and Hölder tilt-stable weak minimizers for a proper lower semicontinuous function f on a Banach space. In terms of the Hölder metric subregularity/regularity of ∂ f, we consider optimality conditions for Hölder weak sharp minimizers and stable Hölder weak sharp minimizers. We prove that x ̄ is a stable Hölder weak sharp minimizer (resp. a Hölder tilt-stable weak minimizer) of f if and only if it is a stable Hölder sharp minimizer (resp. a Hölder tilt-stable minimizer) of f .