A Bregman-Style Improved ADMM and its Linearized Version in the Nonconvex Setting: Convergence and Rate Analyses
This work explores a family of two-block nonconvex optimization problems subject to linear constraints. We first introduce a simple but universal Bregman-style improved alternating direction method of multipliers (ADMM) based on the iteration framework of ADMM and the Bregman distance. Then, we util...
Gespeichert in:
| Veröffentlicht in: | Journal of the Operations Research Society of China (Internet) 2024-06, Vol.12 (2), p.298-340 |
|---|---|
| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 340 |
|---|---|
| container_issue | 2 |
| container_start_page | 298 |
| container_title | Journal of the Operations Research Society of China (Internet) |
| container_volume | 12 |
| creator | Liu, Peng-Jie Jian, Jin-Bao Shao, Hu Wang, Xiao-Quan Xu, Jia-Wei Wu, Xiao-Yu |
| description | This work explores a family of two-block nonconvex optimization problems subject to linear constraints. We first introduce a simple but universal Bregman-style improved alternating direction method of multipliers (ADMM) based on the iteration framework of ADMM and the Bregman distance. Then, we utilize the smooth performance of one of the components to develop a linearized version of it. Compared to the traditional ADMM, both proposed methods integrate a convex combination strategy into the multiplier update step. For each proposed method, we demonstrate the convergence of the entire iteration sequence to a unique critical point of the augmented Lagrangian function utilizing the powerful Kurdyka–Łojasiewicz property, and we also derive convergence rates for both the sequence of merit function values and the iteration sequence. Finally, some numerical results show that the proposed methods are effective and encouraging for the Lasso model. |
| doi_str_mv | 10.1007/s40305-023-00535-8 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3056250157</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3056250157</sourcerecordid><originalsourceid>FETCH-LOGICAL-c270t-ba7b33193ab190a59111b7e9b2b6880a596b990657dcbf12513fdc8bb40b0e33</originalsourceid><addsrcrecordid>eNp9kEtLAzEUhYMoWLR_wFXA9ejNpJmHu1pfhVbBFnEXkpk7Y6TN1CQt1l_vtCO6c3UfnHO49yPkjMEFA0gv_QA4iAhiHgEILqLsgPRilg-iJMmzw98-ez0mfe-NBhFnQiTAemQ1pNcO66Wy0SxsF0jHy5VrNljS4c10SpUtqQmeToxF5cxXu39B501jqbE0vCF9bGzR2A1-0hmGYGx9RUe72dVoC9wHPKuAdGjVYuvRn5KjSi089n_qCZnf3c5HD9Hk6X48Gk6iIk4hRFqlmnOWc6VZDkrkjDGdYq5jnWTZbpHoPIdEpGWhKxYLxquyyLQegAbk_IScd7HtNx9r9EG-N2vX3uBlyyqJBTCRtqq4UxWu8d5hJVfOLJXbSgZyx1Z2bGXLVu7Zyqw18c7kW7Gt0f1F_-P6Br47e80</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3056250157</pqid></control><display><type>article</type><title>A Bregman-Style Improved ADMM and its Linearized Version in the Nonconvex Setting: Convergence and Rate Analyses</title><source>Springer Nature - Complete Springer Journals</source><creator>Liu, Peng-Jie ; Jian, Jin-Bao ; Shao, Hu ; Wang, Xiao-Quan ; Xu, Jia-Wei ; Wu, Xiao-Yu</creator><creatorcontrib>Liu, Peng-Jie ; Jian, Jin-Bao ; Shao, Hu ; Wang, Xiao-Quan ; Xu, Jia-Wei ; Wu, Xiao-Yu</creatorcontrib><description>This work explores a family of two-block nonconvex optimization problems subject to linear constraints. We first introduce a simple but universal Bregman-style improved alternating direction method of multipliers (ADMM) based on the iteration framework of ADMM and the Bregman distance. Then, we utilize the smooth performance of one of the components to develop a linearized version of it. Compared to the traditional ADMM, both proposed methods integrate a convex combination strategy into the multiplier update step. For each proposed method, we demonstrate the convergence of the entire iteration sequence to a unique critical point of the augmented Lagrangian function utilizing the powerful Kurdyka–Łojasiewicz property, and we also derive convergence rates for both the sequence of merit function values and the iteration sequence. Finally, some numerical results show that the proposed methods are effective and encouraging for the Lasso model.</description><identifier>ISSN: 2194-668X</identifier><identifier>EISSN: 2194-6698</identifier><identifier>DOI: 10.1007/s40305-023-00535-8</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Approximation ; Convergence ; Critical point ; Iterative methods ; Lagrange multiplier ; Lagrangian function ; Linearization ; Management Science ; Mathematics ; Mathematics and Statistics ; Multipliers ; Operations Research ; Optimization ; Partial differential equations ; Traffic assignment</subject><ispartof>Journal of the Operations Research Society of China (Internet), 2024-06, Vol.12 (2), p.298-340</ispartof><rights>Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-ba7b33193ab190a59111b7e9b2b6880a596b990657dcbf12513fdc8bb40b0e33</cites><orcidid>0000-0001-8048-7397</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40305-023-00535-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40305-023-00535-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Liu, Peng-Jie</creatorcontrib><creatorcontrib>Jian, Jin-Bao</creatorcontrib><creatorcontrib>Shao, Hu</creatorcontrib><creatorcontrib>Wang, Xiao-Quan</creatorcontrib><creatorcontrib>Xu, Jia-Wei</creatorcontrib><creatorcontrib>Wu, Xiao-Yu</creatorcontrib><title>A Bregman-Style Improved ADMM and its Linearized Version in the Nonconvex Setting: Convergence and Rate Analyses</title><title>Journal of the Operations Research Society of China (Internet)</title><addtitle>J. Oper. Res. Soc. China</addtitle><description>This work explores a family of two-block nonconvex optimization problems subject to linear constraints. We first introduce a simple but universal Bregman-style improved alternating direction method of multipliers (ADMM) based on the iteration framework of ADMM and the Bregman distance. Then, we utilize the smooth performance of one of the components to develop a linearized version of it. Compared to the traditional ADMM, both proposed methods integrate a convex combination strategy into the multiplier update step. For each proposed method, we demonstrate the convergence of the entire iteration sequence to a unique critical point of the augmented Lagrangian function utilizing the powerful Kurdyka–Łojasiewicz property, and we also derive convergence rates for both the sequence of merit function values and the iteration sequence. Finally, some numerical results show that the proposed methods are effective and encouraging for the Lasso model.</description><subject>Approximation</subject><subject>Convergence</subject><subject>Critical point</subject><subject>Iterative methods</subject><subject>Lagrange multiplier</subject><subject>Lagrangian function</subject><subject>Linearization</subject><subject>Management Science</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Multipliers</subject><subject>Operations Research</subject><subject>Optimization</subject><subject>Partial differential equations</subject><subject>Traffic assignment</subject><issn>2194-668X</issn><issn>2194-6698</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEUhYMoWLR_wFXA9ejNpJmHu1pfhVbBFnEXkpk7Y6TN1CQt1l_vtCO6c3UfnHO49yPkjMEFA0gv_QA4iAhiHgEILqLsgPRilg-iJMmzw98-ez0mfe-NBhFnQiTAemQ1pNcO66Wy0SxsF0jHy5VrNljS4c10SpUtqQmeToxF5cxXu39B501jqbE0vCF9bGzR2A1-0hmGYGx9RUe72dVoC9wHPKuAdGjVYuvRn5KjSi089n_qCZnf3c5HD9Hk6X48Gk6iIk4hRFqlmnOWc6VZDkrkjDGdYq5jnWTZbpHoPIdEpGWhKxYLxquyyLQegAbk_IScd7HtNx9r9EG-N2vX3uBlyyqJBTCRtqq4UxWu8d5hJVfOLJXbSgZyx1Z2bGXLVu7Zyqw18c7kW7Gt0f1F_-P6Br47e80</recordid><startdate>20240601</startdate><enddate>20240601</enddate><creator>Liu, Peng-Jie</creator><creator>Jian, Jin-Bao</creator><creator>Shao, Hu</creator><creator>Wang, Xiao-Quan</creator><creator>Xu, Jia-Wei</creator><creator>Wu, Xiao-Yu</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-8048-7397</orcidid></search><sort><creationdate>20240601</creationdate><title>A Bregman-Style Improved ADMM and its Linearized Version in the Nonconvex Setting: Convergence and Rate Analyses</title><author>Liu, Peng-Jie ; Jian, Jin-Bao ; Shao, Hu ; Wang, Xiao-Quan ; Xu, Jia-Wei ; Wu, Xiao-Yu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-ba7b33193ab190a59111b7e9b2b6880a596b990657dcbf12513fdc8bb40b0e33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Approximation</topic><topic>Convergence</topic><topic>Critical point</topic><topic>Iterative methods</topic><topic>Lagrange multiplier</topic><topic>Lagrangian function</topic><topic>Linearization</topic><topic>Management Science</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Multipliers</topic><topic>Operations Research</topic><topic>Optimization</topic><topic>Partial differential equations</topic><topic>Traffic assignment</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Peng-Jie</creatorcontrib><creatorcontrib>Jian, Jin-Bao</creatorcontrib><creatorcontrib>Shao, Hu</creatorcontrib><creatorcontrib>Wang, Xiao-Quan</creatorcontrib><creatorcontrib>Xu, Jia-Wei</creatorcontrib><creatorcontrib>Wu, Xiao-Yu</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of the Operations Research Society of China (Internet)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Peng-Jie</au><au>Jian, Jin-Bao</au><au>Shao, Hu</au><au>Wang, Xiao-Quan</au><au>Xu, Jia-Wei</au><au>Wu, Xiao-Yu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Bregman-Style Improved ADMM and its Linearized Version in the Nonconvex Setting: Convergence and Rate Analyses</atitle><jtitle>Journal of the Operations Research Society of China (Internet)</jtitle><stitle>J. Oper. Res. Soc. China</stitle><date>2024-06-01</date><risdate>2024</risdate><volume>12</volume><issue>2</issue><spage>298</spage><epage>340</epage><pages>298-340</pages><issn>2194-668X</issn><eissn>2194-6698</eissn><abstract>This work explores a family of two-block nonconvex optimization problems subject to linear constraints. We first introduce a simple but universal Bregman-style improved alternating direction method of multipliers (ADMM) based on the iteration framework of ADMM and the Bregman distance. Then, we utilize the smooth performance of one of the components to develop a linearized version of it. Compared to the traditional ADMM, both proposed methods integrate a convex combination strategy into the multiplier update step. For each proposed method, we demonstrate the convergence of the entire iteration sequence to a unique critical point of the augmented Lagrangian function utilizing the powerful Kurdyka–Łojasiewicz property, and we also derive convergence rates for both the sequence of merit function values and the iteration sequence. Finally, some numerical results show that the proposed methods are effective and encouraging for the Lasso model.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s40305-023-00535-8</doi><tpages>43</tpages><orcidid>https://orcid.org/0000-0001-8048-7397</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 2194-668X |
| ispartof | Journal of the Operations Research Society of China (Internet), 2024-06, Vol.12 (2), p.298-340 |
| issn | 2194-668X 2194-6698 |
| language | eng |
| recordid | cdi_proquest_journals_3056250157 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Approximation Convergence Critical point Iterative methods Lagrange multiplier Lagrangian function Linearization Management Science Mathematics Mathematics and Statistics Multipliers Operations Research Optimization Partial differential equations Traffic assignment |
| title | A Bregman-Style Improved ADMM and its Linearized Version in the Nonconvex Setting: Convergence and Rate Analyses |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-30T04%3A46%3A13IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20Bregman-Style%20Improved%20ADMM%20and%20its%20Linearized%20Version%20in%20the%20Nonconvex%20Setting:%20Convergence%20and%20Rate%20Analyses&rft.jtitle=Journal%20of%20the%20Operations%20Research%20Society%20of%20China%20(Internet)&rft.au=Liu,%20Peng-Jie&rft.date=2024-06-01&rft.volume=12&rft.issue=2&rft.spage=298&rft.epage=340&rft.pages=298-340&rft.issn=2194-668X&rft.eissn=2194-6698&rft_id=info:doi/10.1007/s40305-023-00535-8&rft_dat=%3Cproquest_cross%3E3056250157%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3056250157&rft_id=info:pmid/&rfr_iscdi=true |