DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kim, Donghwan | ko |
dc.contributor.author | Fessler, Jeffrey A. | ko |
dc.date.accessioned | 2018-09-18T05:53:45Z | - |
dc.date.available | 2018-09-18T05:53:45Z | - |
dc.date.created | 2018-08-21 | - |
dc.date.created | 2018-08-21 | - |
dc.date.issued | 2016-09 | - |
dc.identifier.citation | MATHEMATICAL PROGRAMMING, v.159, no.1-2, pp.81 - 107 | - |
dc.identifier.issn | 0025-5610 | - |
dc.identifier.uri | http://hdl.handle.net/10203/245453 | - |
dc.description.abstract | We introduce new optimized first-order methods for smooth unconstrained convex minimization. Drori and Teboulle (Math Program 145(1-2):451-482, 2014. doi: 10.1007/s10107-013-0653-0"10.1007/s10107-013-0653-0" TargetType=) recently described a numerical method for computing the N-iteration optimal step coefficients in a class of first-order algorithms that includes gradient methods, heavy-ball methods (Polyak in USSR Comput Math Math Phys 4(5):1-17, 1964. doi: 10.1016/0041-5553(64)90137-510.1016/0041-5553(64)90137-5" TargetType="DOI), and Nesterov's fast gradient methods (Nesterov in Sov Math Dokl 27(2):372-376, 1983; Math Program 103(1):127-152, 2005. doi: 10.1007/s10107-004-0552-510.1007/s10107-004-0552-5" TargetType=). However, the numerical method in Drori and Teboulle (2014) is computationally expensive for large N, and the corresponding numerically optimized first-order algorithm in Drori and Teboulle (2014) requires impractical memory and computation for large-scale optimization problems. In this paper, we propose optimized first-order algorithms that achieve a convergence bound that is two times smaller than for Nesterov's fast gradient methods; our bound is found analytically and refines the numerical bound in Drori and Teboulle (2014). Furthermore, the proposed optimized first-order methods have efficient forms that are remarkably similar to Nesterov's fast gradient methods. | - |
dc.language | English | - |
dc.publisher | SPRINGER HEIDELBERG | - |
dc.title | Optimized first-order methods for smooth convex minimization | - |
dc.type | Article | - |
dc.identifier.wosid | 000382053900003 | - |
dc.identifier.scopusid | 2-s2.0-84945208658 | - |
dc.type.rims | ART | - |
dc.citation.volume | 159 | - |
dc.citation.issue | 1-2 | - |
dc.citation.beginningpage | 81 | - |
dc.citation.endingpage | 107 | - |
dc.citation.publicationname | MATHEMATICAL PROGRAMMING | - |
dc.identifier.doi | 10.1007/s10107-015-0949-3 | - |
dc.contributor.localauthor | Kim, Donghwan | - |
dc.contributor.nonIdAuthor | Fessler, Jeffrey A. | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | First-order algorithms | - |
dc.subject.keywordAuthor | Convergence bound | - |
dc.subject.keywordAuthor | Smooth convex minimization | - |
dc.subject.keywordAuthor | Fast gradient methods | - |
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