Low-order methods for nonconvex functional constrained optimization

Authors
Li, Zichong
ORCID
https://orcid.org/0000-0001-7267-0415
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Other Contributors
Xu, Yangyang
Lai, Rongjie
Mitchell, John E.
Gittens, Alex
Xu, Yangyang
Issue Date
2022-07
Keywords
Mathematics
Degree
PhD
Terms of Use
Attribution-NonCommercial-NoDerivs 3.0 United States
This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute (RPI), Troy, NY. Copyright of original work retained by author.
Full Citation
Abstract
Recently, many real-world problems in engineering and data science not only have very large scales and complicated functional constraints, but also go beyond the scope of convex optimization and inevitably include nonconvex structures. This thesis focuses on developing and analyzing low-order methods for nonconvex functional constrained optimization. In this thesis, I propose several low-order methods, and analyze the complexity of the proposed methods for finding near-KKT points of nonconvex composite problems with either convex or nonconvex functional constraints. All proposed methods generally combine the frameworks of the augmented Lagrangian method, the proximal point method, and my designed subroutines to solve certain unconstrained subproblems. The best-known complexity results are established to all proposed methods on corresponding classes of problems. Numerical experiments demonstrate the efficiency of the proposed methods on a large number of both classical optimization problems and real-world machine learning examples.
Description
July 2022
School of Science
Department
Dept. of Mathematical Sciences
Publisher
Rensselaer Polytechnic Institute, Troy, NY
Relationships
Rensselaer Theses and Dissertations Online Collection
Access
CC BY-NC-ND. Users may download and share copies with attribution in accordance with a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 license. No commercial use or derivatives are permitted without the explicit approval of the author.