{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:26:19Z","timestamp":1787336779852,"version":"build-2736575974"},"reference-count":10,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Optim."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>The feasible set M in general semi-infinite programming (GSIP) need not be closed. This fact is well known. We introduce a natural constraint qualification, called symmetric Mangasarian\u2013Fromovitz constraint qualification (Sym-MFCQ). The Sym-MFCQ is a nontrivial extension of the well-known (extended) MFCQ for the special case of semi-infinite programming (SIP) and disjunctive programming. Under the Sym-MFCQ the closure $\\overline{M}$ has an easy and also natural description. As a consequence, we get a description of the interior and boundary of M. The Sym-MFCQ is shown to be generic and stable under $C^1$-perturbations of the defining functions. For the latter stability the consideration of the closure of M is essential. We introduce an appropriate notion of Karush\u2013Kuhn\u2013Tucker (KKT) points. We show that local minimizers are KKT points under the Sym-MFCQ.<\/jats:p>","DOI":"10.1137\/090775294","type":"journal-article","created":{"date-parts":[[2010,7,1]],"date-time":"2010-07-01T18:03:28Z","timestamp":1278007408000},"page":"2487-2503","source":"Crossref","is-referenced-by-count":14,"title":["General Semi-Infinite Programming: Symmetric Mangasarian\u2013Fromovitz Constraint Qualification and the Closure of the Feasible Set"],"prefix":"10.1137","volume":"20","author":[{"given":"F.","family":"Guerra-V\u00e1zquez","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"H. Th.","family":"Jongen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"V.","family":"Shikhman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,7,1]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2007.02.012"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/s10100-007-0030-2"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/s11590-007-0069-y"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-008-9302-1"},{"key":"R5","unstructured":"M. W. Hirsch,\n                      Differential Topology\n                      , Springer, Berlin, Heidelberg, New York, 1976."},{"key":"R6","doi-asserted-by":"crossref","unstructured":"H. Th. Jongen, P. Jonker, and F. Twilt,\n                      Nonlinear Optimization in Finite Dimensions\n                      , Kluwer Academic, Dordrecht, The Netherlands, 2000.","DOI":"10.1007\/978-1-4615-0017-9"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008282216306"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022650006477"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/S0025-5610(97)00099-3"},{"key":"R10","doi-asserted-by":"crossref","unstructured":"O. Stein,\n                      Bi-level Strategies in Semi-infinite Programming\n                      , Kluwer Academic, Boston, 2003.","DOI":"10.1007\/978-1-4419-9164-5"}],"container-title":["SIAM Journal on Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/090775294","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:30:21Z","timestamp":1787333421000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/090775294"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":10,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/090775294"],"URL":"https:\/\/doi.org\/10.1137\/090775294","relation":{},"ISSN":["1052-6234","1095-7189"],"issn-type":[{"value":"1052-6234","type":"print"},{"value":"1095-7189","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}