<\/p>\n
Title: <\/b>Computation of graphical derivative of solution maps in parameterized quilibria with<\/p>\n
Speaker:\u00a0<\/strong>\u00a0Ji\u0159\u00ed Outrata T\u00edtulo: <\/b>C\u00e1lculo de la derivada gr\u00e1fica de la funci\u00f3n conjunto factible \u00a0en equilibrios parametrizados con restricciones c\u00f3nicas<\/p>\n Ponente:\u00a0<\/strong>\u00a0Ji\u0159\u00ed Outrata Title: Computation of graphical derivative of solution maps in parameterized quilibria with
\nDate:<\/strong>\u00a0\u00a005\/02\/2014 \u00a012:30 h
\nLocation:<\/strong>\u00a0\u00a0Sala de Seminarios, Edificio Torretamarit
\n\u00a0Abstract:<\/strong>
\nThe lecture deals with the computation of the graphical derivative of the solution map in a parameterized generalized equation with a conic constraint set (given as the pre-image of a closed convex cone). Under standard reducibility and nondegeneracy assumptions we compute in the first step the directional derivative of the metric projection onto the constraint set at points, sufficiently close to the reference value of the decision variable. On the basis of this result we are then able to obtain a formula for the desired graphical derivative, provided either the constraint set is convex or fully amenable. In the later situation we make use of an important result concerning the relationship between the projection operator and the (limiting) normal-cone mapping. The obtained graphical derivative formula can be employed in a workable criterion (or even characterization) of the isolated calmness of the solution map which is a valuable stability property. The results are illustrated by simple academic examples involving the ice cream cone
\nKey words. Variational Analysis, graphical derivatives, generalized equations, conic programming.
\nBrief Bio<\/strong>
\nJi\u0159\u00ed Outrata is researcher at the Institute of Information Theory and Automation of the Czech Academy of Sciences. Is author of 3 monographs and over 70 publications in journals, being an associate editor of SIAM Journal on Optimization, Set-Valued and Variational Analysys and Kybernetika. Is an internationally recognized benchmark in the areas of optimization and variational analysis and, among other distinctions, since 2013 he is an associate professor in the School of Information Theory and Mathematical Sciences University of Ballarat in Australia.<\/p>\n
\nDate:<\/strong>\u00a0\u00a005\/02\/2014 \u00a012:30 h
\nLugar:<\/strong>\u00a0\u00a0Sala de Seminarios, Edificio Torretamarit
\nResumen:<\/strong>
\nLa charla trata del c\u00e1lculo de la derivada gr\u00e1fica de la multifunction conjunto soluci\u00f3n de una ecuaci\u00f3n generalizada parametrizada con un conjunto de resticciones c\u00f3nico (dado como la preimagen de un cono convexo cerrado). Bajo hi\u00b4potesis est\u00e1ndar de reducibilidad y no degeneraci\u00f3n, se calcula en un primer paso la derivada direccional de la proyecci\u00f3n m\u00e9trica sobre el conjunto de restricciones en puntos suficientemente pr\u00f3ximos al valor de referencia de la variable de decisi\u00f3n. Ba\u00b4sndonos en este resultado somo capaces de obtener una formula para la derivada gr\u00e1fica buscada, supuesto que, bien el conjunto de restricciones es convexo, o bien es totalmente tratable. En este ultimo caso, hacemos uso de un importante resultado sobre la relaci\u00f3n existente entre el operador proyecci\u00f3n y la multifunci\u00f3n cono normal (l\u00edmite). La formula obtenida para la derivada gr\u00e1fica puede utilizarse en un criterio efectivo (o incluso en una caracterizaci\u00f3n) de la propiedad de \u201c isolated calmness\u201d de la multifunci\u00f3n soluci\u00f3n, que es una propiedad e estabilidad destacada. Los resultados vienen ilustrados con ejemplos acad\u00e9micos sencillos que involucran el llamado \u201ccono de helado\u201d.
\nBreve Biograf\u00eda<\/strong>
\nJi\u0159\u00ed Outrata es investigador del Instituto de Teor\u00eda de la Informaci\u00f3n y Automatizaci\u00f3n de la Academia Checa de las Ciencias. \u00a0Es autor de 3 monograf\u00edas y mas de 70 publicaciones en revistas, siendo asociado de SIAM Journal on Optimization, Set-Valued and \u00a0 Variational Analysys, y Kybernetika.\u00a0Es un referente reconocido internacionalmente en las \u00e1reas de optimizaci\u00f3n y an\u00e1lisis variacional y, entre otras distinciones, desde 2013 es profesor adjunto de la Escuela de Teor\u00eda de la Informaci\u00f3n y Ciencias Matem\u00e1ticas de la Universidad de Ballarat en Australia.<\/p>","protected":false},"excerpt":{"rendered":"
\nSpeaker:\u00a0\u00a0Ji\u0159\u00ed Outrata
\nDate:\u00a0\u00a005\/02\/2014 \u00a012:30 h
\nLocation:\u00a0\u00a0Sala de Seminarios, Edificio Torretamarit
\n\u00a0Abstract:
\nThe lecture deals with the computation of the graphical derivative of the solution map in a parameterized generalized equation with a conic constraint set (given as the pre-image of a closed convex cone). Under standard reducibility and […]<\/p>","protected":false},"author":3477,"featured_media":0,"comment_status":"closed","ping_status":"closed","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\/678"}],"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=678"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/678\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=678"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=678"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=678"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}