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Access Type

WSU Access

Date of Award

1-1-2010

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Mathematics

First Advisor

Boris S. Mordukhovich

Abstract

The dissertation is devoted to the development of variational analysis and generalized differentiation in infinite dimensions. We derive new calculus rules for both first-order partial subdifferentials and second-order partial subdifferentials in the framework of general Banach spaces as well as more developed rules in the framework of Asplund spaces. This calculus is applied in the study of sensitivity analysis for solution maps to the parameterized generalized equations in Asplund spaces, where both bases and fields are parameter-dependent multifunctions. We analyze the parametric sensitivity of either stationary points or stationary point multiplier multifunctions associated with parameterized optimization problems under consideration. The dissertation also focus on a family of parameterized quasi-variational inequalities and conduct a sensitivity analysis for their solution maps.