{"id":26452,"date":"2022-12-12T10:22:18","date_gmt":"2022-12-12T09:22:18","guid":{"rendered":"https:\/\/cio.umh.es\/?p=26452"},"modified":"2022-12-12T10:22:18","modified_gmt":"2022-12-12T09:22:18","slug":"camacho-j-canovas-m-j-parra-j-2022-from-calmness-to-hoffman-constants-for-linear-semi-infinite-inequality-systems-siam-journal-on-optimization-32-42859-2878","status":"publish","type":"post","link":"https:\/\/cio.umh.es\/en\/2022\/12\/12\/camacho-j-canovas-m-j-parra-j-2022-from-calmness-to-hoffman-constants-for-linear-semi-infinite-inequality-systems-siam-journal-on-optimization-32-42859-2878\/","title":{"rendered":"Camacho, J., Canovas, M.J., Parra, J. (2022) &quot;From Calmness To Hoffman Constants For Linear Semi-Infinite Inequality Systems&quot;, SIAM Journal on Optimization, 32 (4):2859\u20132878"},"content":{"rendered":"<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong>Jes\u00fas Camacho, Mar\u00eda Josefa C\u00e1novas and Juan Parra (Center of Operations Research, Miguel Hern\u00e1ndez University of Elche)\u00a0<\/strong><\/p>\n<p class=\"AuthorHeader-module__syvlN margin-size-4-t\" style=\"text-align: justify\"><strong>Abstract: <\/strong>In this paper we focus on different-global, semilocal, and local-versions of Hoffman-type inequalities expressed in a variational form. In a first stage our analysis is developed for generic multifunctions between metric spaces, and we finally deal with the feasible set mapping associated with linear semi-infinite inequality systems (finitely many variables and possibly infinitely many constraints) parameterized by their right-hand sides. The Hoffman modulus is shown to coincide with the Lipschitz upper semicontinuity modulus and the supremum of calmness moduli when confined to multifunctions with a convex graph and closed images in a reflexive Banach space, which is the case for our feasible set mapping. Moreover, for this particular multifunction a formula-involving only the system&#8217;s left-hand side-of the global Hoffman constant is derived, providing a generalization to our semi-infinite context of finite counterparts developed in the literature. In the particular case of locally polyhedral systems, the paper also provides a point-based formula for the (semilocal) Hoffman modulus in terms of the calmness moduli at certain feasible points (extreme points when the nominal feasible set contains no lines), yielding a practically tractable expression for finite systems.<\/p>","protected":false},"excerpt":{"rendered":"<p>Jes\u00fas Camacho, Mar\u00eda Josefa C\u00e1novas and Juan Parra (Center of Operations Research, Miguel Hern\u00e1ndez University of Elche)\u00a0<br \/>\nAbstract: In this paper we focus on different-global, semilocal, and local-versions of Hoffman-type inequalities expressed in a variational form. In a first stage our analysis is developed for generic multifunctions between metric spaces, and we finally deal with the [&#8230;]<\/p>","protected":false},"author":5675,"featured_media":0,"comment_status":"closed","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\/26452"}],"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\/5675"}],"replies":[{"embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/comments?post=26452"}],"version-history":[{"count":0,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/posts\/26452\/revisions"}],"wp:attachment":[{"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/media?parent=26452"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/categories?post=26452"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cio.umh.es\/en\/wp-json\/wp\/v2\/tags?post=26452"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}