Access Type
Open Access Dissertation
Date of Award
January 2015
Degree Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
First Advisor
BORIS MORDUKHOVICH
Abstract
This dissertation focuses on the study and applications of some significant properties in well-posedness and sensitivity analysis, among which the notions of uniform metric regularity , higher-order metric subregularity and its strong subregularity counterpart play an essential role in modern variational analysis. We derived verifiable sufficient conditions and necessary conditions for those notions in terms of appropriate generalized differential as well as geometric constructions of variational analysis. Concrete examples are provided to illustrate the behavior and compare the results. Optimality conditions of parametric variational systems (PVS) under equilibrium constraints are also investigated via the terms of coderivatives. We derived necessary optimality and suboptimality conditions for various problems of constrained optimization and equilibria such as MPECs with amenable/full rank potentials and EPECs with closed preferences in finite-dimensional spaces.
Recommended Citation
Ouyang, Wei, "Well-Posedness Properties In Variational Analysis And Its Applications" (2015). Wayne State University Dissertations. 1349.
https://digitalcommons.wayne.edu/oa_dissertations/1349