{"id":186104,"date":"2011-03-29T00:00:00","date_gmt":"2011-03-31T11:56:03","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/on-a-first-order-primal-dual-algorithm-with-applications-to-convex-problems-in-computer-vision\/"},"modified":"2016-08-22T11:31:41","modified_gmt":"2016-08-22T18:31:41","slug":"on-a-first-order-primal-dual-algorithm-with-applications-to-convex-problems-in-computer-vision","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/on-a-first-order-primal-dual-algorithm-with-applications-to-convex-problems-in-computer-vision\/","title":{"rendered":"On a first-order primal-dual algorithm with applications to convex problems in computer vision"},"content":{"rendered":"<div class=\"asset-content\">\n<p>In the first part of the talk I give new results for a first-order primal-dual algorithm to solve non-smooth convex optimization problems with known saddle-point structure. I show that the algorithm converges to a saddle-point with rate O(1\/N) for the complete class of problems.<br \/>\nFurthermore,<br \/>\nI show that we can get better convergence rates on problems with more regularity.<\/p>\n<p>In the second part of the talk, I discuss new preconditioning techniques for the algorithm. In particular, I propose a family of simple and easy to compute diagonal preconditioners for which convergence of the algorithm is guaranteed without the need to compute any step size parameters.<\/p>\n<p>In the third part of the talk I demonstrate the improved performance of the algorithm by applying it to standard linear programming test problems and a few standard computer vision problems such as image restoration, graph cuts, multi-label image segmentation and optical flow.<\/p>\n<p>(Joint work with Antonin Chambolle, CMAP, Ecole Polytechnique)<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In the first part of the talk I give new results for a first-order primal-dual algorithm to solve non-smooth convex optimization problems with known saddle-point structure. I show that the algorithm converges to a saddle-point with rate O(1\/N) for the complete class of problems. Furthermore, I show that we can get better convergence rates on [&hellip;]<\/p>\n","protected":false},"featured_media":196072,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr_hide_image_in_river":0,"footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-186104","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/o2snIyau6qU","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/186104","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/186104\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/196072"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=186104"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=186104"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=186104"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=186104"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=186104"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=186104"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=186104"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=186104"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=186104"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=186104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}