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- Golden Ratio Algorithms for Variational Inequalities
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Golden Ratio Algorithms for Variational Inequalities Malitsky, Yura
Description
We present several novel methods for solving general (pseudo-) monotone variational inequalities. The first method uses fixed stepsize and is similar to the proximal reflected gradient method: it also requires only one value of operator and one prox-operator per iteration. However, its extension — the dynamic version — has a notable distinction. In every iteration it defines a stepsize, based on a local information about operator, without running any linesearch procedure. Thus, the iteration costs of this method is almost the same as in the first one with a fixed stepsize, but it converges without the Lipschitz assumption on the operator. We further discuss possible generalizations of the methods, in particular for solving large-scale nonlinear saddle point problems. Some numerical experiments are reported.
Item Metadata
Title |
Golden Ratio Algorithms for Variational Inequalities
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-09-18T11:14
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Description |
We present several novel methods for solving general (pseudo-) monotone variational inequalities. The first method uses fixed stepsize and is similar to the proximal reflected gradient method: it also requires only one value of operator and one prox-operator per iteration. However, its extension — the dynamic version — has a notable distinction. In every iteration it defines a stepsize, based on a local information about operator, without running any linesearch procedure. Thus, the iteration costs of this method is almost the same as in the first one with a fixed stepsize, but it converges without the Lipschitz assumption on the operator. We further discuss possible generalizations of the methods, in particular for solving large-scale nonlinear saddle point problems. Some numerical experiments are reported.
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Extent |
35 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Institute for Numerical and Applied Mathematics, University of Goettingen
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Series | |
Date Available |
2018-03-23
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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 |
10.14288/1.0364425
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Postdoctoral
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International