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A parameterized Douglas-Rachford algorithm : theory and applications Wang, Dongying
Abstract
Douglas-Rachford algorithm is important due to its applications on the Heron problem and on the image denoising. Mathematically, it can be considered as finding a point such that the point belongs to a zero set of the sum of two maximally monotone operators. In this thesis, previous work on Douglas-Rachford algorithm is presented and the Douglas-Rachford algorithm with a changed parameter is considered. I give it the name "α-Douglas-Rachford algorithm". The new algorithm which has the changed parameter is shown to have a convergent result and other conclusions similar to those of the classic Douglas-Rachford algorithm. At the same time, it has been shown that the application of the α-Douglas-Rachford algorithm is wider than the application of the classic one. Later on, the α-Douglas-Rachford algorithm is proved to converge to the solution of the composited monotone inclusion problems, and in a special-limit case, it has some other properties. The numerical experiments confirm that the α-Douglas-Rachford algorithm does have the properties that I proved theoretically.
Item Metadata
Title |
A parameterized Douglas-Rachford algorithm : theory and applications
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2017
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Description |
Douglas-Rachford algorithm is important due to its applications on the Heron problem and on the image denoising. Mathematically, it can be considered as finding a point such that the point belongs to a zero set of the sum of two maximally monotone operators.
In this thesis, previous work on Douglas-Rachford algorithm is presented and the Douglas-Rachford algorithm with a changed parameter is considered. I give it the name "α-Douglas-Rachford algorithm". The new algorithm which has the changed parameter is shown to have a convergent result and other conclusions similar to those of the classic Douglas-Rachford algorithm. At the same time, it has been shown that the application of the α-Douglas-Rachford algorithm is wider than the application of the classic one.
Later on, the α-Douglas-Rachford algorithm is proved to converge to the solution of the composited monotone inclusion problems, and in a special-limit case, it has some other properties. The numerical experiments confirm that the α-Douglas-Rachford algorithm does have the properties that I proved theoretically.
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Genre | |
Type | |
Language |
eng
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Date Available |
2017-08-18
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0354491
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2017-09
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Campus | |
Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International