{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:38:34Z","timestamp":1787341114260,"version":"3.56.0"},"reference-count":10,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2013,1]]},"abstract":"<jats:p>For a boundedly generated drop $[a,E]$ (a property which holds, for instance, whenever $E$ is bounded), where $a$ belongs to a real Banach space $X$ and $E \\subset X$ is a nonempty convex set, we show that for every lower semicontinuous function $h:X\\longrightarrow {\\mathbb{R}}\\cup \\{+\\infty\\}$ that satisfies $\\sup_ {\\delta&gt;0} \\inf_{x\\in E+\\delta B_X }h(x)&gt;h(a)$ ($B_X$ being the unitary open ball in $X$), there exists $\\bar x \\in [a,E]$ such that $h(a)\\ge h(\\bar x)$ and $\\bar x$ is a strict minimizer of $h$ on the drop $[\\bar x,E]$.<\/jats:p>","DOI":"10.1137\/120875934","type":"journal-article","created":{"date-parts":[[2013,6,10]],"date-time":"2013-06-10T00:52:11Z","timestamp":1370825531000},"page":"1154-1166","source":"Crossref","is-referenced-by-count":2,"title":["Existence of Minimizers on Drops"],"prefix":"10.1137","volume":"23","author":[{"given":"R.","family":"Correa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P.","family":"Gajardo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L.","family":"Thibault","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D.","family":"Zagrodny","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2013,6,10]]},"reference":[{"key":"atypb1","unstructured":"J. M. Borwein and Q. J. Zhu,<i>Techniques of Variational Analysis<\/i> CMS Books Math.\/ Ouvrages Math. SMC 20, Springer-Verlag, New York, 2005."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/080738271"},{"key":"atypb3","first-page":"381","volume":"46","author":"Dancs S.","year":"1983","journal-title":"Acta Sci. Math. (Szeged)"},{"key":"atypb4","first-page":"369","volume":"6","author":"Dane\u0161 J.","year":"1972","journal-title":"Boll. Union Mat. Ital. (4)"},{"key":"atypb5","first-page":"443","volume":"26","author":"Dane\u0161 J.","year":"1985","journal-title":"Comment. Math. Univ. Carolin."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(74)90025-0"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1080\/02331939208843858"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(86)90069-6"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.4064\/sm-85-1-17-35"},{"key":"atypb10","first-page":"653","volume":"53","author":"Turinici M.","year":"1981","journal-title":"An. Acad. Brasil. Ci\u00eanc."}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/120875934","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:06:16Z","timestamp":1787339176000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/120875934"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1]]},"references-count":10,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,1]]}},"alternative-id":["10.1137\/120875934"],"URL":"https:\/\/doi.org\/10.1137\/120875934","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1]]}}}