{"id":192489,"date":"2015-07-17T00:00:00","date_gmt":"2015-07-17T22:21:37","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/a-faster-cutting-plane-method-and-its-implications-for-combinatorial-and-convex-optimization\/"},"modified":"2024-10-02T08:58:25","modified_gmt":"2024-10-02T15:58:25","slug":"a-faster-cutting-plane-method-and-its-implications-for-combinatorial-and-convex-optimization","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/a-faster-cutting-plane-method-and-its-implications-for-combinatorial-and-convex-optimization\/","title":{"rendered":"A Faster Cutting Plane Method and its Implications for Combinatorial and Convex Optimization"},"content":{"rendered":"<div class=\"asset-content\">\n<p>In this talk, I will present a new algorithm for finding a point in a convex set given a separation oracle. In particular, given a separation oracle for a convex set K in Rn that is contained in a box of radius R, I will show how to either compute a point in K or prove that K does not contain a ball of radius eps using an expected O(n log(nR\/eps)) evaluations of the oracle and additional time O~(n<sup>3<\/sup>). This improves upon the O~(n<sup>3<\/sup>.373) additional time of the previous fastest algorithm achieved over 25 years ago by Vaidya.<\/p>\n<p>As an example, I will show how to use it to obtain a faster algorithm for the following problems: 1. Submodular Function Minimization 2. Submodular Flow 3. Matroid Intersection 4. Semidefinite Programming<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this talk, I will present a new algorithm for finding a point in a convex set given a separation oracle. In particular, given a separation oracle for a convex set K in Rn that is contained in a box of radius R, I will show how to either compute a point in K or [&hellip;]<\/p>\n","protected":false},"featured_media":199136,"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":[13561],"msr-video-type":[206954],"msr-locale":[268875],"msr-post-option":[],"msr-session-type":[],"msr-impact-theme":[],"msr-pillar":[],"msr-episode":[],"msr-research-theme":[],"class_list":["post-192489","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-algorithms","msr-video-type-microsoft-research-talks","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/vLROghdusCM","msr_secondary_video_url":"","msr_video_file":"http:\/\/0","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/192489","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":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/192489\/revisions"}],"predecessor-version":[{"id":1089669,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/192489\/revisions\/1089669"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/199136"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=192489"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=192489"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=192489"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=192489"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=192489"},{"taxonomy":"msr-session-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-session-type?post=192489"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=192489"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=192489"},{"taxonomy":"msr-episode","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-episode?post=192489"},{"taxonomy":"msr-research-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-theme?post=192489"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}