자료유형  

 학위논문

Control Number  

0017161412

International Standard Book Number  

9798382842714

Dewey Decimal Classification Number  

519

Main Entry-Personal Name  

Jiang, Liwei.

Publication, Distribution, etc. (Imprint  

[S.l.] : Cornell University., 2024

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2024

Physical Description  

311 p.

General Note  

Source: Dissertations Abstracts International, Volume: 85-12, Section: B.

General Note  

Advisor: Davis, Damek.

Dissertation Note  

Thesis (Ph.D.)--Cornell University, 2024.

Summary, Etc.  

요약Optimization-based algorithms are the foundation for empirically successful methods in modern fields, such as artificial intelligence and data science. Although classical optimization theory provides guarantees for functions with smoothness or convexity, a significant portion of modern problems do not possess any of these. Despite the worst-case examples where efficient algorithms are unavailable, typical nonsmoothness arises with a "partly smooth" structure, meaning that they are well-behaved relative to a smooth "active manifold."This thesis develops and analyzes first-order algorithms based on the aforementioned nonsmooth structure. We first develop two regularity conditions describing how sub-gradients interact with active manifolds and then show that they hold for a broad and generic class of functions. With these cornerstones, we demonstrate that when randomly perturbed or equipped with stochastic noise, subgradient methods only converge to minimizers of generic, Clarke regular semialgebraic problems. When convergence to a certain minimizer is known, we demonstrate that stochastic (projected) subgradient methods have asymptotic normality, making them asymptotically optimal algorithms in the locally minimax sense of Hajek and Le Cam.These findings culminate with a new first-order algorithm-NTDescent-which exhibits local nearly linear convergence on typical nonsmooth functions with quadratic growth. The convergence rate of NTDescent depends only on the function's intrinsic quantities but not the problem's underlying dimension.

Subject Added Entry-Topical Term  

Applied mathematics.

Subject Added Entry-Topical Term  

Statistics.

Index Term-Uncontrolled  

Asymptotic normality

Index Term-Uncontrolled  

First-order method

Index Term-Uncontrolled  

Linear convergence

Index Term-Uncontrolled  

Nonsmooth optimization

Index Term-Uncontrolled  

Parameter-free

Index Term-Uncontrolled  

Saddle point avoidance

Added Entry-Corporate Name  

Cornell University Operations Research and Information Engineering

Host Item Entry  

Dissertations Abstracts International. 85-12B.

Electronic Location and Access  

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Control Number  

joongbu:658036