{"id":13240,"date":"2019-02-27T11:30:28","date_gmt":"2019-02-27T11:30:28","guid":{"rendered":"http:\/\/cio.edu.umh.es\/?p=13240"},"modified":"2019-02-27T11:30:28","modified_gmt":"2019-02-27T11:30:28","slug":"an-approach-to-calmness-of-linear-inequality-systems-from-farkas-lemma-2019-optimization-letters-springer-13-295-307","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2019\/02\/27\/an-approach-to-calmness-of-linear-inequality-systems-from-farkas-lemma-2019-optimization-letters-springer-13-295-307\/","title":{"rendered":"An approach to calmness of linear inequality systems from Farkas lemma (2019). Optimization Letters (Springer), 13, 295-307."},"content":{"rendered":"<p>[:es]<strong>Mar\u00eda Josefa C\u00e1novas\u00a0<\/strong>(<em>Miguel Hern\u00e1ndez University of Elche<\/em>),\u00a0<strong>N. Dinh\u00a0<\/strong>(<em>International University of Vietnam<\/em>),\u00a0<strong>D. H. Long<\/strong> (<em>Tien Giang University<\/em>)\u00a0and<strong>\u00a0Juan\u00a0Parra<\/strong>\u00a0(<em>Miguel Hern\u00e1ndez University of Elche<\/em><em>).<\/em><br \/>\n<strong>Abstract.<\/strong>\u00a0We deal with the feasible set mapping of linear inequality systems under right-hand side perturbations. From a version of Farkas lemma for difference of convex functions, we derive an operative relationship between calmness constants for this mapping at a nominal solution and associated neighborhoods where such constants work. We also provide illustrative examples where this approach allows us to compute the sharp Hoffman constant at the nominal system.<br \/>\n<strong>Keywords.<\/strong>\u00a0Calmness; Hoffman constants; Local error bounds; Global error bounds; Feasible set mapping; Linear programming; Variational analysis[:]<\/p>","protected":false},"excerpt":{"rendered":"<p>[:es]Mar\u00eda Josefa C\u00e1novas\u00a0(Miguel Hern\u00e1ndez University of Elche),\u00a0N. Dinh\u00a0(International University of Vietnam),\u00a0D. H. Long (Tien Giang University)\u00a0and\u00a0Juan\u00a0Parra\u00a0(Miguel Hern\u00e1ndez University of Elche).<br \/>\nAbstract.\u00a0We deal with the feasible set mapping of linear inequality systems under right-hand side perturbations. From a version of Farkas lemma for difference of convex functions, we derive an operative relationship between calmness constants for this [&#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":[369888],"tags":[],"_links":{"self":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/13240"}],"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=13240"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/13240\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=13240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=13240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=13240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}