{"id":10574,"date":"2018-05-17T10:50:15","date_gmt":"2018-05-17T10:50:15","guid":{"rendered":"http:\/\/cio.edu.umh.es\/?p=10574"},"modified":"2018-05-17T10:50:15","modified_gmt":"2018-05-17T10:50:15","slug":"seminario-de-jan-j-ruckmann","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2018\/05\/17\/seminario-de-jan-j-ruckmann\/","title":{"rendered":"Seminario de Jan J. R\u00fcckmann"},"content":{"rendered":"<p>[:es]<span style=\"color: #000000\"><strong>Speaker:\u00a0<\/strong>Jan J. R\u00fcckmann<\/span><br \/>\n<span style=\"color: #000000\"><strong>Title:\u00a0<\/strong>\u201cMathematical Programs with Complementarity constraints: Critical Point Theory\u201d<\/span><br \/>\n<span style=\"color: #000000\"><strong>Coauthors:\u00a0<\/strong>Hubertus Th. Jongen and Vladimir Shikhman.<\/span><br \/>\n<span style=\"color: #000000\"><strong>Date: <\/strong>23 May.\u00a0 12:30 h.<\/span><br \/>\n<span style=\"color: #000000\"><strong>Localication:<\/strong>\u00a0Sala de Seminarios (Edificio Torretamarit)<\/span><br \/>\n<span style=\"color: #000000\"><strong>Abstract<\/strong>.\u00a0We study mathematical programs with complementarity constraints from a topological point of view. We derive a Morse Lemma at nondegenerate C- stationary points and present two basic theorems from Morse theory (deformation theorem and cell-attachment theorem). Outside the C-stationary point set, continuous deformation of lower level sets can be performed and, as a consequence, the topological data (such as the number of connected components) remain invariant. However, when passing a level containing a C-stationary point, the topology of the lower level set changes via the attachment of a q-dimensional cell where its dimension equals the stationary C-index of the corresponding C- stationary point. The stationary C-index depends on both the restricted Hessian of the Lagrangian and the Lagrange multipliers related to bi-active complementarity constraints. Finally, some relations with other stationarity concepts are discussed.<\/span><br \/>\n<span style=\"color: #000000\">The lecture is based on a joint paper with Hubertus Th. Jongen and Vladimir Shikhman.<\/span>[:]<\/p>","protected":false},"excerpt":{"rendered":"<p>[:es]Speaker:\u00a0Jan J. R\u00fcckmann<br \/>\nTitle:\u00a0\u201cMathematical Programs with Complementarity constraints: Critical Point Theory\u201d<br \/>\nCoauthors:\u00a0Hubertus Th. Jongen and Vladimir Shikhman.<br \/>\nDate: 23 May.\u00a0 12:30 h.<br \/>\nLocalication:\u00a0Sala de Seminarios (Edificio Torretamarit)<br \/>\nAbstract.\u00a0We study mathematical programs with complementarity constraints from a topological point of view. We derive a Morse Lemma at nondegenerate C- stationary points and present two basic theorems from Morse theory (deformation theorem [&#8230;]<\/p>","protected":false},"author":3477,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[4,873],"tags":[],"_links":{"self":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/10574"}],"collection":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/users\/3477"}],"replies":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/comments?post=10574"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/10574\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=10574"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=10574"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=10574"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}