{"id":951,"date":"2018-08-13T15:46:20","date_gmt":"2018-08-13T23:46:20","guid":{"rendered":"http:\/\/depts.washington.edu\/uwrainlab\/?page_id=951"},"modified":"2018-08-17T13:12:46","modified_gmt":"2018-08-17T21:12:46","slug":"bregman-parallel-direction-method-of-multipliers-for-distributed-optimization-via-mirror-averaging","status":"publish","type":"page","link":"https:\/\/depts.washington.edu\/uwrainlab\/bregman-parallel-direction-method-of-multipliers-for-distributed-optimization-via-mirror-averaging\/","title":{"rendered":"Bregman Parallel Direction Method of Multipliers for Distributed Optimization via Mirror Averaging"},"content":{"rendered":"<p><strong>Y. Yu, B. A\u00e7\u0131kme\u015fe, M. Mesbahi<\/strong><\/p>\n<p><strong>IEEE Control Systems Letters<\/strong><\/p>\n<div class=\"gs_scl\">\n<div id=\"gsc_vcd_descr\" class=\"gsc_vcd_value\">Distributed optimization aims to optimize a global objective formed by a sum of coupled local convex functions over a graph via only local computation and communication. In this letter, we propose the Bregman parallel direction method of multipliers (PDMM) based on a generalized averaging step named mirror averaging. We establish the global convergence and O(1\/T) convergence rate of the Bregman PDMM, along with its O(n\/ ln n) improvement over existing PDMM, where T denotes the number of iterations and n the dimension of solution variable. In addition, we can enhance its performance by optimizing the spectral gap of the averaging matrix. We demonstrate our results via a numerical example.<\/div>\n<\/div>\n<div class=\"gs_scl\"><\/div>\n<p><strong>Links:<\/strong><\/p>\n<p><a href=\"https:\/\/ieeexplore.ieee.org\/document\/8354719\/\"><img loading=\"lazy\" class=\"alignnone wp-image-810\" src=\"http:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/download.png\" alt=\"\" width=\"26\" height=\"26\" srcset=\"https:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/download.png 225w, https:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/download-150x150.png 150w\" sizes=\"(max-width: 26px) 100vw, 26px\" \/><\/a> \u00a0 <a href=\"https:\/\/ieeexplore.ieee.org\/stamp\/stamp.jsp?arnumber=8354719\"><img loading=\"lazy\" class=\"alignnone wp-image-811\" src=\"http:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/image_preview.png\" alt=\"\" width=\"31\" height=\"31\" srcset=\"https:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/image_preview.png 250w, https:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/image_preview-150x150.png 150w\" sizes=\"(max-width: 31px) 100vw, 31px\" \/><\/a> \u00a0 <a href=\"https:\/\/scholar.google.com\/scholar?hl=en&amp;as_sdt=0%2C48&amp;q=Bregman+Parallel+Direction+Method+of+Multipliers+for+Distributed+Optimization+via+Mirror+Averaging+&amp;btnG=#d=gs_cit&amp;p=&amp;u=%2Fscholar%3Fq%3Dinfo%3Ao-Iq61rXMgAJ%3Ascholar.google.com%2F%26output%3Dcite%26scirp%3D0%26hl%3Den\"><img loading=\"lazy\" class=\"alignnone wp-image-809\" src=\"http:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/BibTeX_logo.svg_-300x97.png\" alt=\"\" width=\"65\" height=\"21\" srcset=\"https:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/BibTeX_logo.svg_-300x97.png 300w, https:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/BibTeX_logo.svg_-768x248.png 768w, https:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/BibTeX_logo.svg_-1024x330.png 1024w, https:\/\/depts.washington.edu\/uwrainlab\/wordpress\/wp-content\/uploads\/2018\/07\/BibTeX_logo.svg_.png 1200w\" sizes=\"(max-width: 65px) 100vw, 65px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Y. Yu, B. A\u00e7\u0131kme\u015fe, M. Mesbahi IEEE Control Systems Letters Distributed optimization aims to optimize a global objective formed by a sum of coupled local convex functions over a graph via only local computation and communication. In this letter, we propose the Bregman parallel direction method of multipliers (PDMM) based on a generalized averaging step [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/pages\/951"}],"collection":[{"href":"https:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/comments?post=951"}],"version-history":[{"count":3,"href":"https:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/pages\/951\/revisions"}],"predecessor-version":[{"id":988,"href":"https:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/pages\/951\/revisions\/988"}],"wp:attachment":[{"href":"https:\/\/depts.washington.edu\/uwrainlab\/wp-json\/wp\/v2\/media?parent=951"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}