{"id":652653,"date":"2020-04-26T23:13:12","date_gmt":"2020-04-27T06:13:12","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-project&#038;p=652653"},"modified":"2020-04-26T23:23:14","modified_gmt":"2020-04-27T06:23:14","slug":"accelerated-bregman-proximal-gradient-methods","status":"publish","type":"msr-project","link":"https:\/\/www.microsoft.com\/en-us\/research\/project\/accelerated-bregman-proximal-gradient-methods\/","title":{"rendered":"Accelerated Bregman Proximal Gradient Methods"},"content":{"rendered":"<p>A Python package of accelerated first-order algorithms for solving relatively-smooth convex optimization problems<\/p>\n<pre><code>minimize { f(x) + P(x) | x in C }\r\n<\/code><\/pre>\n<p>with a reference function h(x), where C is a closed convex set and<\/p>\n<ul>\n<li>h(x) is convex and essentially smooth on C;<\/li>\n<li>f(x) is convex and differentiable, and L-smooth relative to h(x), that is, f(x)-L*h(x) is convex;<\/li>\n<li>P(x) is convex and closed (lower semi-continuous).<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p>Publication:<\/p>\n<p><a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" href=\"https:\/\/arxiv.org\/abs\/1808.03045\">https:\/\/arxiv.org\/abs\/1808.03045<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/p>\n<p>Github repository:<\/p>\n<p><a class=\"msr-external-link glyph-append glyph-append-open-in-new-tab glyph-append-xsmall\" href=\"https:\/\/github.com\/Microsoft\/accbpg\">https:\/\/github.com\/Microsoft\/accbpg<span class=\"sr-only\"> (opens in new tab)<\/span><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A Python package of accelerated first-order algorithms for solving relatively-smooth convex optimization problems<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"research-area":[13561,13556],"msr-locale":[268875],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-652653","msr-project","type-msr-project","status-publish","hentry","msr-research-area-algorithms","msr-research-area-artificial-intelligence","msr-locale-en_us","msr-archive-status-active"],"msr_project_start":"2018-09-01","related-publications":[500003],"related-downloads":[],"related-videos":[],"related-groups":[],"related-events":[],"related-opportunities":[],"related-posts":[],"related-articles":[],"tab-content":[],"slides":[],"related-researchers":[],"msr_research_lab":[199565],"msr_impact_theme":[],"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/652653"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-project"}],"version-history":[{"count":2,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/652653\/revisions"}],"predecessor-version":[{"id":652665,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/652653\/revisions\/652665"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=652653"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=652653"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=652653"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=652653"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=652653"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}