Variational Analysis In Parametric Optimization

<p>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.</p>

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Open Access Dissertation

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2010

Author dc:creator

• Nguyen Thi, Yen Nhi

Contributors dc:contributor

• Boris S. Mordukhovich

• coderivative
• parametric optimization
• quasi-variational inequality
• sensitivity analysis
• set-valued mapping
• subdifferential
• Mathematics

Repository record dc:identifier

https://digitalcommons.wayne.edu/oa_dissertations/181

OAI identifier oai:identifier

oai:digitalcommons.wayne.edu:oa_dissertations-1180