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Operator Splitting Methods for Conve...
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Liu, Yanli.
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Operator Splitting Methods for Convex and Nonconvex Optimization.
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Operator Splitting Methods for Convex and Nonconvex Optimization./
作者:
Liu, Yanli.
出版者:
Ann Arbor : ProQuest Dissertations & Theses, : 2020,
面頁冊數:
232 p.
附註:
Source: Dissertations Abstracts International, Volume: 81-11, Section: B.
Contained By:
Dissertations Abstracts International81-11B.
標題:
Applied mathematics. -
電子資源:
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27962470
ISBN:
9798645427412
Operator Splitting Methods for Convex and Nonconvex Optimization.
Liu, Yanli.
Operator Splitting Methods for Convex and Nonconvex Optimization.
- Ann Arbor : ProQuest Dissertations & Theses, 2020 - 232 p.
Source: Dissertations Abstracts International, Volume: 81-11, Section: B.
Thesis (Ph.D.)--University of California, Los Angeles, 2020.
This item must not be sold to any third party vendors.
This dissertation focuses on a family of optimization methods called operator splitting methods. They solve complicated problems by decomposing the problem structure into simpler pieces and make progress on each of them separately. Over the past two decades, there has been a resurgence of interests in these methods as the demand for solving structured large-scale problems grew. One of the major challenges for splitting methods is their sensitivity to ill-conditioning, which often makes them struggle to achieve a high order of accuracy. Furthermore, their classical analyses are restricted to the nice settings where solutions do exist, and everything is convex. Much less is known when either of these assumptions breaks down.This work aims to address the issues above. Specifically, we propose a novel acceleration technique called inexact preconditioning, which exploits second-order information at relatively low computation cost. We also show that certain splitting methods still work on problems without solutions, in the sense that their iterates provide information on what goes wrong and how to fix. Finally, for nonconvex problems with saddle points, we show that almost surely, splitting methods will only converge to the local minimums under certain assumptions.
ISBN: 9798645427412Subjects--Topical Terms:
2122814
Applied mathematics.
Subjects--Index Terms:
Convex optimization
Operator Splitting Methods for Convex and Nonconvex Optimization.
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This dissertation focuses on a family of optimization methods called operator splitting methods. They solve complicated problems by decomposing the problem structure into simpler pieces and make progress on each of them separately. Over the past two decades, there has been a resurgence of interests in these methods as the demand for solving structured large-scale problems grew. One of the major challenges for splitting methods is their sensitivity to ill-conditioning, which often makes them struggle to achieve a high order of accuracy. Furthermore, their classical analyses are restricted to the nice settings where solutions do exist, and everything is convex. Much less is known when either of these assumptions breaks down.This work aims to address the issues above. Specifically, we propose a novel acceleration technique called inexact preconditioning, which exploits second-order information at relatively low computation cost. We also show that certain splitting methods still work on problems without solutions, in the sense that their iterates provide information on what goes wrong and how to fix. Finally, for nonconvex problems with saddle points, we show that almost surely, splitting methods will only converge to the local minimums under certain assumptions.
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