Fully Stable Well-posedness And Fully Stable Minimum With Respect To An Admissible Function

The concepts of H（?）lder sharp/weak sharp minimizers and H（?）lder tilt-stable minima have been widely studied and applied in optimization theory.For example,the concept of H（?）lder sharp/weak sharp minimizers has been recognized to be useful in the algorithm convergence analysis and mathematical programming,while stability is widely used in the study of optimal solutions to conventional nonlinear programming problems and solutions to generalized equations and variational inequalities.In this thesis,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 H（?）lder minimizers by Zheng and Ng [SIAM J.Optim.,2015;25:416–438] and the fully stable H（?）lder 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 thesis provide insight into necessary or sufficient conditions for tiltstable minimizers in Asplund spaces and therefore generalize some existing ones in the recent literature.