Abstract:<\/strong><\/p>\n This talk presents fast optimization algorithms from the viewpoint of continuous dynamical systems. Venue:<\/strong> Sala John Von Neumann, 7th floor, Beauchef 851<\/p>\n","protected":false},"excerpt":{"rendered":" Ra\u00fal Tintaya (CMM, U. de Chile) <\/p>\n","protected":false},"author":136,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[5],"tags":[],"class_list":["post-755","post","type-post","status-publish","format-standard","hentry","category-past-seminar"],"_links":{"self":[{"href":"https:\/\/eventos.cmm.uchile.cl\/postdocseminars\/wp-json\/wp\/v2\/posts\/755","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eventos.cmm.uchile.cl\/postdocseminars\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/eventos.cmm.uchile.cl\/postdocseminars\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/postdocseminars\/wp-json\/wp\/v2\/users\/136"}],"replies":[{"embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/postdocseminars\/wp-json\/wp\/v2\/comments?post=755"}],"version-history":[{"count":9,"href":"https:\/\/eventos.cmm.uchile.cl\/postdocseminars\/wp-json\/wp\/v2\/posts\/755\/revisions"}],"predecessor-version":[{"id":790,"href":"https:\/\/eventos.cmm.uchile.cl\/postdocseminars\/wp-json\/wp\/v2\/posts\/755\/revisions\/790"}],"wp:attachment":[{"href":"https:\/\/eventos.cmm.uchile.cl\/postdocseminars\/wp-json\/wp\/v2\/media?parent=755"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/postdocseminars\/wp-json\/wp\/v2\/categories?post=755"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/eventos.cmm.uchile.cl\/postdocseminars\/wp-json\/wp\/v2\/tags?post=755"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nWe begin with the classical correspondence between gradient flow and gradient descent, and then discuss how nonsmooth gradient flows naturally lead to proximal-type methods.
\nThe main focus is on inertial dynamical systems, where second-order terms introduce memory and momentum into the optimization process.
\nThrough this perspective, we explain how continuous-time models such as the heavy-ball system and Nesterov-type dynamics provide insight into acceleration, damping, stability, and convergence of fast first-order methods.
\nWe also discuss how these ideas can be extended beyond standard minimization problems, including recent directions for nonconvex minimax optimization.<\/p>\n