Fully stable well-posedness and fully stable minimum with respect to an admissible function. (1st September 2020)

• Record Type: Journal Article
• Authors: Zhu, Jiangxing; Arthur Köbis, Markus; Hu, Chunhai; He, Qinghai; Li, Jiaxiong
• Is Part Of: Optimization. Volume 69:Number 9(2020)
• Page Start: 2085
• Page End: 2107
• Publication Date: 2020-09-01
• Subjects: Admissible function -- fully stable well-posedness -- fully stable minimum -- tilt stability; 90C31 -- 90C30 -- 49K40 -- 49J52; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1751159
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, the notions of fully stable well-posedness and fully stable minimum of optimization problems with an extended real-valued objective function in an Asplund space setting are considered, where the objective function undergoes both tilt perturbations and general parameter perturbations. Special cases of the first notion reduce to the stable Hölder minimizers by Zheng and Ng [SIAM J Optim. 2015;25:416–438] and the fully stable Hölder minimizers introduced by Zheng, Zhu and Ng [SIAM J Optim. 2018;28:2601–2624], respectively. By using techniques of variational analysis and generalized differentiation, the results presented in this paper provide insight into necessary or sufficient conditions for tilt-stable minimizers of nonlinear programmes in Asplund spaces and therefore generalize some existing ones in the recent literature.