{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T07:54:48Z","timestamp":1719474888184},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2012,3,30]],"date-time":"2012-03-30T00:00:00Z","timestamp":1333065600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Math Sci"],"published-print":{"date-parts":[[2012,4]]},"DOI":"10.1007\/s10958-012-0734-2","type":"journal-article","created":{"date-parts":[[2012,3,29]],"date-time":"2012-03-29T00:59:45Z","timestamp":1332982785000},"page":"126-143","source":"Crossref","is-referenced-by-count":10,"title":["Optimality criteria without constraint qualifications for linear semidefinite problems"],"prefix":"10.1007","volume":"182","author":[{"given":"O. I.","family":"Kostyukova","sequence":"first","affiliation":[]},{"given":"T. V.","family":"Tchemisova","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,3,30]]},"reference":[{"key":"734_CR1","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511810800","volume-title":"Matrix Algebra: Econometric Exercises, Vol. 1","author":"KM Abadir","year":"2005","unstructured":"K. M. Abadir and J. R. Magnus, Matrix Algebra: Econometric Exercises, Vol. 1, Cambridge Univ. Press (2005)."},{"issue":"1","key":"734_CR2","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF00933262","volume":"25","author":"R Abrams","year":"1978","unstructured":"R. Abrams and L. Kerzner, \u201cA simplified test for optimality,\u201d J. Optim. Theory Appl., 25, No. 1, 161\u2013170 (1978).","journal-title":"J. Optim. Theory Appl."},{"key":"734_CR3","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1137\/0805002","volume":"5","author":"F Alizadeh","year":"1995","unstructured":"F. Alizadeh, \u201cInterior point methods in semidefinite programming with applications to combinatorial optimization,\u201d SIAM J. Optim., 5, 13\u201351 (1995).","journal-title":"SIAM J. Optim."},{"issue":"3","key":"734_CR4","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1002\/nav.3800270307","volume":"27","author":"A Ben Tal","year":"1980","unstructured":"A. Ben Tal, L. Kerzner, and S. Zlobec, \u201cOptimality conditions for convex semi-infinite programming problems,\u201d Naval Res. Logist., 27, No. 3, 413\u2013435 (1980).","journal-title":"Naval Res. Logist."},{"key":"734_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1394-9","volume-title":"Perturbation Analysis of Optimization Problems","author":"JF Bonnans","year":"2000","unstructured":"J. F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems, Springer-Verlag, New York (2000)."},{"key":"734_CR6","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/BFb0120983","volume":"19","author":"JM Borwein","year":"1982","unstructured":"J. M. Borwein and H.Wolkowicz, \u201cCharacterizations of optimality without constraint qualification for the abstract convex program,\u201d Math. Prog. Stud., 19, 77\u2013100 (1982).","journal-title":"Math. Prog. Stud."},{"issue":"5\u20136","key":"734_CR7","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1080\/02331930600816080","volume":"55","author":"MD Fajardo","year":"2006","unstructured":"M. D. Fajardo and M. A. L\u00f3pez, \u201cSome results about the facial geometry of convex semi-infinite systems,\u201d Optimization, 55, Nos. 5\u20136, 661\u2013684 (2006).","journal-title":"Optimization"},{"key":"734_CR8","unstructured":"G. Gruber, S. Kruk, F. Rendl, and H. Wolkowicz, \u201cPresolving for semidefinite program without constraints qualifications,\u201d in: Proc. of the Second Workshop on High Perfomance Optimization Techniques (G. Gruber et al. eds.), Rotterdam, Netherlands (1997)."},{"key":"734_CR9","unstructured":"S.-A. Gustafson and K. O. Kortanek, \u201cSemi-infinite programming and applications,\u201d in: Proc. 11 Int. Symp. \u201cMathematical Programming,\u201d Bonn 1982, (1983), pp. 132\u2013157."},{"key":"734_CR10","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1137\/1035089","volume":"35","author":"R Hettich","year":"1993","unstructured":"R. Hettich and K. O. Kortanek, Semi-infinite programming: theory, methods and applications,\u201d SIAM Rev., 35, (1993), 380\u2013429.","journal-title":"SIAM Rev."},{"issue":"2","key":"734_CR11","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1137\/S1052623402417699","volume":"14","author":"V Jeyakumar","year":"2003","unstructured":"V. Jeyakumar, G. M. Lee, and N. Dihn, \u201cNew sequential Lagrange multiplier conditions characterizing optimality without constraint qualification for convex programs,\u201d SIAM J. Optim., 14, No. 2, 534\u2013547 (2003).","journal-title":"SIAM J. Optim."},{"key":"734_CR12","unstructured":"K. O. Kortanek and V. G. Medvedev, \u201cSemi-infinite programming and new applications in finance,\u201d in: Encyclopedia of Optimization (C. Floudas and P. Pardalos, eds.), Kluwer Academic (2005)."},{"key":"734_CR13","unstructured":"O. I. Kostyukova, Investigation of the linear extremal problems with continuum constraints [in Russian], Preprint No. 26 (336), Institute of Mathematics, Academy of Sciences of BSSR, Minsk, Belarus (1988)."},{"issue":"2","key":"734_CR14","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1080\/10556780902992803","volume":"25","author":"OI Kostyukova","year":"2010","unstructured":"O. I. Kostyukova and T. V. Tchemisova, \u201cSufficient optimality conditions for convex semi-infinite programming,\u201d Optim. Methods Software, 25, No. 2, 279\u2013297 (2010).","journal-title":"Optim. Methods Software"},{"issue":"8","key":"734_CR15","first-page":"13","volume":"13","author":"OI Kostyukova","year":"2008","unstructured":"O. I. Kostyukova, T. V. Tchemisova, and S. A. Yermalinskaya, \u201cOn the algorithm of determination of immobile indices for convex SIP problems,\u201d Int. J. Math. Stat., 13, No. J08, 13\u201333 (2008).","journal-title":"Int. J. Math. Stat."},{"key":"734_CR16","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970791","volume-title":"Interior Point Polynomial Algorithms in Convex Programming: Theory and Algorithms","author":"YE Nesterov","year":"1994","unstructured":"Y. E. Nesterov and A. S. Nemirovskii, Interior Point Polynomial Algorithms in Convex Programming: Theory and Algorithms, SIAM, Philadelphia, PA (1994)."},{"key":"734_CR17","unstructured":"M. V. Ramana, An exact duality theory for semi-definite programming and its complexity implications, DIMACS Technical report 95-02R, RUTCOR, Rutgers University, New Brunswick, NJ (1995)."},{"issue":"3","key":"734_CR18","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1137\/S1052623495288350","volume":"7","author":"MV Ramana","year":"1997","unstructured":"M. V. Ramana, L. Tuncel, and H. Wolkowicz, \u201cStrong duality for semi-definite programming,\u201d SIAM J. Optim., 7, No. 3, 641\u2013662 (1997).","journal-title":"SIAM J. Optim."},{"key":"734_CR19","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/0024-3795(85)90182-X","volume":"67","author":"A Shapiro","year":"1985","unstructured":"A. Shapiro, \u201cExtremal problems on the set of negative definite matrices,\u201d Lin. Algebra Appl., 67, 7\u201318 (1985).","journal-title":"Lin. Algebra Appl."},{"key":"734_CR20","unstructured":"L. Vandenberghe and S. Boyd, \u201cConnection between semi-infinite and semi-definite programming,\u201d in: Semi-Infinite Programming (R. Reemtsen and J.-J. Rueckmann, Eds.), Kluwer Academic (1998)."},{"issue":"3","key":"734_CR21","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/BF00933505","volume":"40","author":"H Wolkowicz","year":"1983","unstructured":"H. Wolkowicz, \u201cMethod of reduction in convex programming,\u201d J. Optim. Theory Appl., 40, No. 3, 349\u2013378 (1983).","journal-title":"J. Optim. Theory Appl."},{"key":"734_CR22","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/S0166-218X(01)00352-3","volume":"123","author":"H Wolkowicz","year":"2002","unstructured":"H. Wolkowicz and M. F. Anjos, \u201cSemi-definite programming for discrete optimization and matrix completion problems,\u201d Discr. Appl. Math., 123, 513\u2013577 (2002).","journal-title":"Discr. Appl. Math."},{"key":"734_CR23","doi-asserted-by":"crossref","unstructured":"H. Wolkowicz, R. Saigal, and L. Vandenberghe, Handbook of Semidefinite Programming. Theory, Algorithms, and Applications, Kluwer Academic (2000).","DOI":"10.1007\/978-1-4615-4381-7"}],"container-title":["Journal of Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10958-012-0734-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10958-012-0734-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10958-012-0734-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,26]],"date-time":"2019-06-26T05:55:41Z","timestamp":1561528541000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10958-012-0734-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,30]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,4]]}},"alternative-id":["734"],"URL":"https:\/\/doi.org\/10.1007\/s10958-012-0734-2","relation":{},"ISSN":["1072-3374","1573-8795"],"issn-type":[{"value":"1072-3374","type":"print"},{"value":"1573-8795","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3,30]]}}}