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Access Type
WSU Access
Date of Award
January 2024
Degree Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
First Advisor
Boris S. Mordukhovich
Abstract
This dissertation proposes and develops new Newton-type methods to solve nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and generalized differentiation. The objective functions belong to a broad class of prox-regular functions with specification to constrained optimization of convex and nonconvex structured sums. The proposed algorithms are formulated in terms of the second-order subdifferential of such functions that enjoy extensive calculus rules and can be efficiently computed for broad classes of extended-real-valued functions. Further applications and numerical experiments are conducted for the Lassoproblems, the box constrained problems of quadratic programming, and the fast best subset selection problems, which play a crucial role in statistics and machine learning.
Recommended Citation
Vo, Thanh Phat, "Generalized Coderivative-Based Newtonian Methods In Nonsmooth Nonconvex Optimization And Applications" (2024). Wayne State University Dissertations. 4064.
https://digitalcommons.wayne.edu/oa_dissertations/4064