Understanding the accelerated proximal point method for strongly monotone operator = 강단조 연산자를 이용하는 가속화된 근위점 알고리즘에 대한 이해

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The thesis studies acceleration of the proximal point method for strongly monotone operators, based on the accelerated proximal point method for monotone operators. We introduce a variant of the accelerated proximal point method for strongly monotone operator problems. We analyze the variant by two approaches, the bilinear analysis and the performance estimation problem approach. This variant has fast convergence rate for strongly monotone operator with some appropriately chosen parameters. In the bilinear analysis, we find eigenvalues related to the convergence rate of the variant of accelerated proximal point method. In the performance estimation problem approach, we present that the variant of accelerated proximal point method achieves a linear convergence rate for some carefully chosen parameters. Also, we numerically show that the variant of accelerated proximal point method is faster than proximal point method with specific parameter setting.
Advisors
Kim, donghwanresearcher김동환researcher
Description
한국과학기술원 :수리과학과,
Publisher
한국과학기술원
Issue Date
2020
Identifier
325007
Language
eng
Description

학위논문(석사) - 한국과학기술원 : 수리과학과, 2020.8,[iii, 20 p. :]

Keywords

accelerated proximal point method▼aconvergence rate▼aperformance estimation problem▼astrongly monotone▼abilinear; 가속화된 근위 점 알고리즘▼a수렴 속도▼a성능 측정 문제▼a강단조▼a쌍 선형

URI
http://hdl.handle.net/10203/284972
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=925132&flag=dissertation
Appears in Collection
MA-Theses_Master(석사논문)
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