- Title
- About regularity properties in variational analysis and applications in optimization
- Creator
- Nguyen, Hieu Thao
- Date
- 2015
- Type
- Text; Thesis; PhD
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/99995
- Identifier
- vital:10457
- Identifier
- http://library.federation.edu.au/record=b2679977
- Abstract
- Regularity properties lie at the core of variational analysis because of their importance for stability analysis of optimization and variational problems, constraint qualications, qualication conditions in coderivative and subdierential calculus and convergence analysis of numerical algorithms. The thesis is devoted to investigation of several research questions related to regularity properties in variational analysis and their applications in convergence analysis and optimization. Following the works by Kruger, we examine several useful regularity properties of collections of sets in both linear and Holder-type settings and establish their characterizations and relationships to regularity properties of set-valued mappings. Following the recent publications by Lewis, Luke, Malick (2009), Drusvyatskiy, Ioe, Lewis (2014) and some others, we study application of the uniform regularity and related properties of collections of sets to alternating projections for solving nonconvex feasibility problems and compare existing results on this topic. Motivated by Ioe (2000) and his subsequent publications, we use the classical iteration scheme going back to Banach, Schauder, Lyusternik and Graves to establish criteria for regularity properties of set-valued mappings and compare this approach with the one based on the Ekeland variational principle. Finally, following the recent works by Khanh et al. on stability analysis for optimization related problems, we investigate calmness of set-valued solution mappings of variational problems.; Doctor of Philosophy
- Publisher
- Federation University Australia
- Rights
- Copyright Hieu Thao Nguyen
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- Regularity properties; Variational analysis; Optimization
- Full Text
- Thesis Supervisor
- Kruger, Alexander
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