Access Type
Open Access Dissertation
Date of Award
January 2013
Degree Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
First Advisor
Boris Mordukhovich
Abstract
The dissertation concerns a systematic study of full stability in general optimization models including its conventional Lipschitzian version as well as the new Holderian one. We derive various characterizations of both Lipschitzian and Holderian full stability in nonsmooth optimization, which are new in finite-dimensional and infinite-dimensional frameworks. The characterizations obtained are given in terms of second-order growth conditions and also via second-order generalized differential constructions of variational analysis. We develop effective applications of our general characterizations of full stability to
parametric variational systems including the well-known generalized equations and variational inequalities. Many relationships of full stability with the conventional notions of strong regularity and strong stability are established for a large class of problems of constrained optimization with twice continuously differentiable data. Other applications of full stability to nonlinear programming, to semidefinite programming, and to optimal control problems governed by semilinear elliptic PDEs are also studied.
Recommended Citation
Tran, Nghia, "Full Stability In Optimization" (2013). Wayne State University Dissertations. 801.
https://digitalcommons.wayne.edu/oa_dissertations/801