{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,30]],"date-time":"2025-03-30T04:20:44Z","timestamp":1743308444861},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2015,2,12]],"date-time":"2015-02-12T00:00:00Z","timestamp":1423699200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2016,4]]},"DOI":"10.1007\/s10898-015-0277-4","type":"journal-article","created":{"date-parts":[[2015,2,11]],"date-time":"2015-02-11T04:07:44Z","timestamp":1423627664000},"page":"679-702","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Generalized Farkas\u2019 lemma and gap-free duality for minimax DC optimization with polynomials and robust quadratic optimization"],"prefix":"10.1007","volume":"64","author":[{"given":"V.","family":"Jeyakumar","sequence":"first","affiliation":[]},{"given":"G. M.","family":"Lee","sequence":"additional","affiliation":[]},{"given":"N. T. H.","family":"Linh","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,2,12]]},"reference":[{"key":"277_CR1","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s10479-004-5022-1","volume":"133","author":"LTH An","year":"2005","unstructured":"An, L.T.H., Tao, P.D.: The DC (difference of convex functions) programming and DCA revisited with DC models of real world non-convex optimization problems. Ann. Oper. Res. 133, 23\u201346 (2005)","journal-title":"Ann. Oper. Res."},{"key":"277_CR2","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1023\/A:1014813701864","volume":"22","author":"EG Belousov","year":"2002","unstructured":"Belousov, E.G., Klatte, D.: A Frank\u2013Wolfe type theorem for convex polynomial programs. Comp. Optim. Appl. 22, 37\u201348 (2002)","journal-title":"Comp. Optim. Appl."},{"key":"277_CR3","volume-title":"Robust Optimization. Princeton Series in Applied Mathematics","author":"A Ben-Tal","year":"2009","unstructured":"Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton Series in Applied Mathematics. Princeton University Press, Princeton, NJ (2009)"},{"key":"277_CR4","first-page":"595608","volume":"39","author":"R Bot","year":"2007","unstructured":"Bot, R., Hodrea, I., Wanka, G.: Some new Farkas-type results for inequality systems with DC functions. J. Glob. Optim. 39, 595608 (2007)","journal-title":"J. Glob. Optim."},{"issue":"3\u20134","key":"277_CR5","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1080\/02331930801951348","volume":"59","author":"N Dinh","year":"2010","unstructured":"Dinh, N., Nghia, T.T.A., Vallet, G.: Closedness condition and its applications to DC programs with convex constraints. Optimization 59(3\u20134), 541\u2013560 (2010)","journal-title":"Optimization"},{"key":"277_CR6","first-page":"235","volume":"15","author":"N Dinh","year":"2008","unstructured":"Dinh, N., Vallet, G., Nghia, T.T.A.: Farkas-type results and duality for DC programs with convex constraints. J. Convex Anal. 15, 235\u2013262 (2008)","journal-title":"J. Convex Anal."},{"issue":"1","key":"277_CR7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11750-014-0319-y","volume":"22","author":"N Dinh","year":"2014","unstructured":"Dinh, N., Jeyakumar, V.: Farkas\u2019 lemma: three decades of generalizations for mathematical optimization. TOP 22(1), 1\u201322 (2014)","journal-title":"TOP"},{"issue":"3","key":"277_CR8","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1137\/100789749","volume":"21","author":"DH Fang","year":"2011","unstructured":"Fang, D.H., Li, C., Yang, X.Q.: Stable and total Fenchel duality for DC optimization problems in locally convex spaces. SIAM J. Optim. 21(3), 730\u2013760 (2011)","journal-title":"SIAM J. Optim."},{"key":"277_CR9","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1016\/j.jmaa.2014.04.017","volume":"418","author":"R Harada","year":"2014","unstructured":"Harada, R., Kuroiwa, D.: Lagrange-type duality in DC programming. J. Math. Anal. Appl. 418, 415\u2013424 (2014)","journal-title":"J. Math. Anal. Appl."},{"key":"277_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02796-7","volume-title":"Convex Analysis and Minimization Algorithms. I. Fundamentals","author":"J-B Hiriart-Urruty","year":"1993","unstructured":"Hiriart-Urruty, J.-B., Lemar\u00e9chal, C.: Convex Analysis and Minimization Algorithms. I. Fundamentals, vol. 305. Springer, Berlin (1993)"},{"key":"277_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1023\/A:1021765131316","volume":"103","author":"R Horst","year":"1999","unstructured":"Horst, R., Thoai, N.V.: DC programming: overview. J. Optim. Theory Appl. 103, 1\u201343 (1999)","journal-title":"J. Optim. Theory Appl."},{"key":"277_CR12","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s10107-007-0104-x","volume":"114","author":"V Jeyakumar","year":"2008","unstructured":"Jeyakumar, V., Lee, G.M.: Complete characterization of stable Farkas\u2019 lemma and cone-convex programming duality. Math. Program. 114, 335\u2013347 (2008)","journal-title":"Math. Program."},{"key":"277_CR13","doi-asserted-by":"crossref","unstructured":"Jeyakumar, V., Li, G.: A new class of alternative theorems for SOS-convex inequalities and robust optimization. Appl. Anal. 94(1), 56\u201374 (2015)","DOI":"10.1080\/00036811.2013.859251"},{"issue":"2","key":"277_CR14","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s10898-012-9857-8","volume":"55","author":"V Jeyakumar","year":"2013","unstructured":"Jeyakumar, V., Li, G.: Robust solutions of quadratic optimization over single quadratic constraint under interval uncertainty. J. Glob. Optim. 55(2), 209\u2013226 (2013)","journal-title":"J. Glob. Optim."},{"issue":"3","key":"277_CR15","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1007\/s10957-013-0496-0","volume":"162","author":"V Jeyakumar","year":"2014","unstructured":"Jeyakumar, V., Vicente-P\u00e9rez, J.: Dual semidefinite programs without duality gaps for a class of convex minimax programs. J. Optim. Theory Appl. 162(3), 735\u2013753 (2014)","journal-title":"J. Optim. Theory Appl."},{"key":"277_CR16","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1006\/jmaa.1999.6496","volume":"237","author":"JE Martinez-Legaz","year":"1999","unstructured":"Martinez-Legaz, J.E., Volle, M.: Duality in DC programming: the case of several DC constraints. J. Math. Anal. Appl. 237, 657\u2013671 (1999)","journal-title":"J. Math. Anal. Appl."},{"key":"277_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4614-4538-8","volume-title":"Calculus Without Derivatives, Graduate Texts in Mathematics","author":"J-P Penot","year":"2013","unstructured":"Penot, J.-P.: Calculus Without Derivatives, Graduate Texts in Mathematics, vol. 266. Springer, New York (2013)"},{"key":"277_CR18","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1137\/S003614450444614X","volume":"49","author":"I Polik","year":"2007","unstructured":"Polik, I., Terlaky, T.: A survey of the S-lemma. SIAM Rev. 49, 371\u2013418 (2007)","journal-title":"SIAM Rev."},{"key":"277_CR19","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton, NJ (1970)"},{"key":"277_CR20","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/0022-247X(78)90243-3","volume":"66","author":"JF Toland","year":"1978","unstructured":"Toland, J.F.: Duality in nonconvex optimization. J. Math. Anal. Appl. 66, 399\u2013415 (1978)","journal-title":"J. Math. Anal. Appl."},{"key":"277_CR21","doi-asserted-by":"crossref","DOI":"10.1142\/5021","volume-title":"Convex Analysis in General Vector Spaces","author":"C Zalinescu","year":"2002","unstructured":"Zalinescu, C.: Convex Analysis in General Vector Spaces. World Scientific, Singapore (2002)"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-015-0277-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-015-0277-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-015-0277-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,20]],"date-time":"2019-08-20T17:00:51Z","timestamp":1566320451000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-015-0277-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,12]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,4]]}},"alternative-id":["277"],"URL":"https:\/\/doi.org\/10.1007\/s10898-015-0277-4","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,12]]}}}