Full Stability In Optimization

<p>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 </p> <p>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.</p>

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Open Access Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2013

Author dc:creator

• Tran, Nghia

Contributors dc:contributor

• Boris Mordukhovich

• Mathematics

Repository record dc:identifier

https://digitalcommons.wayne.edu/oa_dissertations/801

OAI identifier oai:identifier

oai:digitalcommons.wayne.edu:oa_dissertations-1800