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New Perspectives on Continuous Optimization : = Theory and Methodology.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	New Perspectives on Continuous Optimization :/
其他題名:	Theory and Methodology.
作者:	Zhao, Shipu.
面頁冊數:	1 online resource (219 pages)
附註:	Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
Contained By:	Dissertations Abstracts International84-12B.
標題:	Applied mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30312922click for full text (PQDT)
ISBN:	9798379710330

New Perspectives on Continuous Optimization : = Theory and Methodology.
Zhao, Shipu.

New Perspectives on Continuous Optimization :Theory and Methodology. - 1 online resource (219 pages)

Source: Dissertations Abstracts International, Volume: 84-12, Section: B.

Thesis (Ph.D.)--Cornell University, 2023.

Includes bibliographical references

Large-scale continuous optimization arises in many practical problems such as machine learning, signal processing, and imaging. It is usually challenging to analyze the theoretical properties of optimization algorithms and design scalable algorithms that work well in practice. This dissertation provides new perspectives on continuous optimization in both theory and methodology. From the theoretical side, we present a framework for reasoning about equivalence between a broad class of iterative convex continuous optimization algorithms. The notion of algorithm equivalence can make it easier to understand the connections between optimization algorithms, relate many analytical properties of interest such as convergence or robustness, and further give insights to design new algorithms. From the methodological side, we first present NysADMM, a scalable algorithm for faster composite convex optimization by exploiting the low-rank structure. NysADMM accelerates the inexact linearized Alternating Direction Method of Multipliers (ADMM) by constructing a preconditioner for the ADMM subproblem from a randomized low-rank Nystrom approximation. ¨ Second, we present GeNI-ADMM, a framework generalized from NysADMM, which encompasses any ADMM algorithm that solves a first- or (generalized) second-order approximation to the ADMM subproblem and allows inexact sub-problem solves. It facilitates the theoretical analysis of various approximate ADMM schemes for large-scale composite convex optimization.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798379710330Subjects--Topical Terms:

2122814
Applied mathematics.
Subjects--Index Terms:

Algorithm equivalenceIndex Terms--Genre/Form:

542853
Electronic books.

New Perspectives on Continuous Optimization : = Theory and Methodology.
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504 $a Includes bibliographical references
520 $a Large-scale continuous optimization arises in many practical problems such as machine learning, signal processing, and imaging. It is usually challenging to analyze the theoretical properties of optimization algorithms and design scalable algorithms that work well in practice. This dissertation provides new perspectives on continuous optimization in both theory and methodology. From the theoretical side, we present a framework for reasoning about equivalence between a broad class of iterative convex continuous optimization algorithms. The notion of algorithm equivalence can make it easier to understand the connections between optimization algorithms, relate many analytical properties of interest such as convergence or robustness, and further give insights to design new algorithms. From the methodological side, we first present NysADMM, a scalable algorithm for faster composite convex optimization by exploiting the low-rank structure. NysADMM accelerates the inexact linearized Alternating Direction Method of Multipliers (ADMM) by constructing a preconditioner for the ADMM subproblem from a randomized low-rank Nystrom approximation. ¨ Second, we present GeNI-ADMM, a framework generalized from NysADMM, which encompasses any ADMM algorithm that solves a first- or (generalized) second-order approximation to the ADMM subproblem and allows inexact sub-problem solves. It facilitates the theoretical analysis of various approximate ADMM schemes for large-scale composite convex optimization.
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538 $a Mode of access: World Wide Web
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