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dc.rights.licenseCC 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.
dc.contributorXu, Yangyang
dc.contributorLai, Rongjie
dc.contributorMitchell, John E.
dc.contributorGittens, Alex
dc.contributor.advisorXu, Yangyang
dc.contributor.authorLi, Zichong
dc.date.accessioned2022-09-26T22:08:53Z
dc.date.available2022-09-26T22:08:53Z
dc.date.issued2022-07
dc.identifier.urihttps://hdl.handle.net/20.500.13015/6256
dc.descriptionJuly 2022
dc.descriptionSchool of Science
dc.description.abstractRecently, 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.
dc.languageENG
dc.language.isoen_US
dc.publisherRensselaer Polytechnic Institute, Troy, NY
dc.relation.ispartofRensselaer Theses and Dissertations Online Collection
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/us/*
dc.subjectMathematics
dc.titleLow-order methods for nonconvex functional constrained optimization
dc.typeElectronic thesis
dc.typeThesis
dc.date.updated2022-09-26T22:08:55Z
dc.rights.holderThis electronic version is a licensed copy owned by Rensselaer Polytechnic Institute (RPI), Troy, NY. Copyright of original work retained by author.
dc.creator.identifierhttps://orcid.org/0000-0001-7267-0415
dc.description.degreePhD
dc.relation.departmentDept. of Mathematical Sciences


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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.
Except where otherwise noted, this item's license is described as 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.