Fully stable well-posedness and fully stable minimum with respect to an admissible function

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.