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Conference Paper: Adaptive primal-dual splitting methods for statistical learning and image processing
Title | Adaptive primal-dual splitting methods for statistical learning and image processing |
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Authors | |
Issue Date | 2015 |
Citation | Advances in Neural Information Processing Systems, 2015, v. 2015-January, p. 2089-2097 How to Cite? |
Abstract | The alternating direction method of multipliers (ADMM) is an important tool for solving complex optimization problems, but it involves minimization sub-steps that are often difficult to solve efficiently. The Primal-Dual Hybrid Gradient (PDHG) method is a powerful alternative that often has simpler sub-steps than ADMM, thus producing lower complexity solvers. Despite the flexibility of this method, PDHG is often impractical because it requires the careful choice of multiple stepsize parameters. There is often no intuitive way to choose these parameters to maximize efficiency, or even achieve convergence. We propose self-adaptive stepsize rules that automatically tune PDHG parameters for optimal convergence. We rigorously analyze our methods, and identify convergence rates. Numerical experiments show that adaptive PDHG has strong advantages over non-adaptive methods in terms of both efficiency and simplicity for the user. |
Persistent Identifier | http://hdl.handle.net/10722/251157 |
ISSN | 2020 SCImago Journal Rankings: 1.399 |
DC Field | Value | Language |
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dc.contributor.author | Goldstein, Thomas | - |
dc.contributor.author | Li, Min | - |
dc.contributor.author | Yuan, Xiaoming | - |
dc.date.accessioned | 2018-02-01T01:54:46Z | - |
dc.date.available | 2018-02-01T01:54:46Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | Advances in Neural Information Processing Systems, 2015, v. 2015-January, p. 2089-2097 | - |
dc.identifier.issn | 1049-5258 | - |
dc.identifier.uri | http://hdl.handle.net/10722/251157 | - |
dc.description.abstract | The alternating direction method of multipliers (ADMM) is an important tool for solving complex optimization problems, but it involves minimization sub-steps that are often difficult to solve efficiently. The Primal-Dual Hybrid Gradient (PDHG) method is a powerful alternative that often has simpler sub-steps than ADMM, thus producing lower complexity solvers. Despite the flexibility of this method, PDHG is often impractical because it requires the careful choice of multiple stepsize parameters. There is often no intuitive way to choose these parameters to maximize efficiency, or even achieve convergence. We propose self-adaptive stepsize rules that automatically tune PDHG parameters for optimal convergence. We rigorously analyze our methods, and identify convergence rates. Numerical experiments show that adaptive PDHG has strong advantages over non-adaptive methods in terms of both efficiency and simplicity for the user. | - |
dc.language | eng | - |
dc.relation.ispartof | Advances in Neural Information Processing Systems | - |
dc.title | Adaptive primal-dual splitting methods for statistical learning and image processing | - |
dc.type | Conference_Paper | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.scopus | eid_2-s2.0-84965146424 | - |
dc.identifier.volume | 2015-January | - |
dc.identifier.spage | 2089 | - |
dc.identifier.epage | 2097 | - |
dc.identifier.issnl | 1049-5258 | - |