Modified Fejér sequences and applications
In this note, we propose and study the notion of modified Fejér sequences. Within a Hilbert space setting, this property has been used to prove ergodic convergence of proximal incremental subgradient methods. Here we show that indeed it provides a unifying framework to prove convergence rates for ob...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer US
2018
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| Online Access: | http://hdl.handle.net/1721.1/117359 https://orcid.org/0000-0001-6376-4786 |
| _version_ | 1826201333453029376 |
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| author | Lin, Junhong Rosasco, Lorenzo Villa, Silvia Zhou, Ding-Xuan |
| author2 | Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences Lin, Junhong Rosasco, Lorenzo Villa, Silvia Zhou, Ding-Xuan |
| author_sort | Lin, Junhong |
| collection | MIT |
| description | In this note, we propose and study the notion of modified Fejér sequences. Within a Hilbert space setting, this property has been used to prove ergodic convergence of proximal incremental subgradient methods. Here we show that indeed it provides a unifying framework to prove convergence rates for objective function values of several optimization algorithms. In particular, our results apply to forward–backward splitting algorithm, incremental subgradient proximal algorithm, and the Douglas–Rachford splitting method including and generalizing known results. |
| first_indexed | 2024-09-23T11:49:58Z |
| format | Article |
| id | mit-1721.1/117359 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:49:58Z |
| publishDate | 2018 |
| publisher | Springer US |
| record_format | dspace |
| spelling | mit-1721.1/1173592022-10-01T06:21:16Z Modified Fejér sequences and applications Lin, Junhong Rosasco, Lorenzo Villa, Silvia Zhou, Ding-Xuan Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences Rosasco, Lorenzo In this note, we propose and study the notion of modified Fejér sequences. Within a Hilbert space setting, this property has been used to prove ergodic convergence of proximal incremental subgradient methods. Here we show that indeed it provides a unifying framework to prove convergence rates for objective function values of several optimization algorithms. In particular, our results apply to forward–backward splitting algorithm, incremental subgradient proximal algorithm, and the Douglas–Rachford splitting method including and generalizing known results. Italy. Ministry of Education, University, Scientific and Technological Research (FIRB Project RBFR12M3AC) 2018-08-14T17:52:33Z 2018-09-02T05:00:05Z 2017-11 2018-08-08T04:08:09Z Article http://purl.org/eprint/type/JournalArticle 0926-6003 1573-2894 http://hdl.handle.net/1721.1/117359 Lin, Junhong, et al. “Modified Fejér Sequences and Applications.” Computational Optimization and Applications, vol. 71, no. 1, Sept. 2018, pp. 95–113. https://orcid.org/0000-0001-6376-4786 en https://doi.org/10.1007/s10589-017-9962-1 Computational Optimization and Applications Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer Science+Business Media, LLC application/pdf Springer US Springer US |
| spellingShingle | Lin, Junhong Rosasco, Lorenzo Villa, Silvia Zhou, Ding-Xuan Modified Fejér sequences and applications |
| title | Modified Fejér sequences and applications |
| title_full | Modified Fejér sequences and applications |
| title_fullStr | Modified Fejér sequences and applications |
| title_full_unstemmed | Modified Fejér sequences and applications |
| title_short | Modified Fejér sequences and applications |
| title_sort | modified fejer sequences and applications |
| url | http://hdl.handle.net/1721.1/117359 https://orcid.org/0000-0001-6376-4786 |
| work_keys_str_mv | AT linjunhong modifiedfejersequencesandapplications AT rosascolorenzo modifiedfejersequencesandapplications AT villasilvia modifiedfejersequencesandapplications AT zhoudingxuan modifiedfejersequencesandapplications |