{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T07:10:07Z","timestamp":1769584207031,"version":"3.49.0"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,7,31]],"date-time":"2013-07-31T00:00:00Z","timestamp":1375228800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2014,5]]},"DOI":"10.1007\/s10898-013-0091-9","type":"journal-article","created":{"date-parts":[[2013,7,30]],"date-time":"2013-07-30T12:41:45Z","timestamp":1375188105000},"page":"41-58","source":"Crossref","is-referenced-by-count":10,"title":["Multiobjective DC programs with infinite convex constraints"],"prefix":"10.1007","volume":"59","author":[{"given":"Shaojian","family":"Qu","sequence":"first","affiliation":[]},{"given":"Mark","family":"Goh","sequence":"additional","affiliation":[]},{"given":"Soon-Yi","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Robert","family":"De Souza","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,7,31]]},"reference":[{"key":"91_CR1","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/s10107-009-0323-4","volume":"123","author":"N Dinh","year":"2010","unstructured":"Dinh, N., Mordukhovich, B., Nghia, T.T.A.: Subdifferentials of value functions and optimality conditions for DC and bilevel infinite and semi-infinite programs. Math. Program. Ser. B 123, 101\u2013138 (2010)","journal-title":"Math. Program. Ser. B"},{"key":"91_CR2","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1051\/cocv:2007027","volume":"13","author":"N Dinh","year":"2007","unstructured":"Dinh, N., Goberna, M.A., L\u00f3pez, M.A., Son, T.Q.: New Farkas-type results with applications to convex infinite programs. ESAIM Control Optim. Calc. Var. 13, 580\u2013597 (2007)","journal-title":"ESAIM Control Optim. Calc. Var."},{"key":"91_CR3","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1080\/02331930902730070","volume":"58","author":"A Shapiro","year":"2009","unstructured":"Shapiro, A.: Semi-infinite programs, duality, discretization and optimality conditions. Optimization 58, 133\u2013161 (2009)","journal-title":"Optimization"},{"key":"91_CR4","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s10898-004-8266-z","volume":"30","author":"DH Li","year":"2004","unstructured":"Li, D.H., Qi, L.Q., Tam, J., Wu, S.Y.: A smoothing Newton method for semi-infinite programs. J. Glob. Optim. 30, 169\u2013194 (2004)","journal-title":"J. Glob. Optim."},{"key":"91_CR5","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s10898-004-8274-z","volume":"30","author":"CF Chen","year":"2004","unstructured":"Chen, C.F., Wu, S.Y.: Duality theorems and algorithms for linear programs in measure spaces. J. Glob. Optim. 30, 207\u2013233 (2004)","journal-title":"J. Glob. Optim."},{"key":"91_CR6","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/j.ejor.2006.08.045","volume":"180","author":"M L\u00f3pez","year":"2007","unstructured":"L\u00f3pez, M., Still, G.: Semi-infinite programs. Eur. J. Oper. Res. 180, 491\u2013518 (2007)","journal-title":"Eur. J. Oper. Res."},{"key":"91_CR7","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/s10957-009-9514-7","volume":"142","author":"NJ Huang","year":"2009","unstructured":"Huang, N.J., Li, J., Wu, S.Y.: Optimality conditions for vector optimization problems. J. Optim. Theory Appl. 142, 323\u2013342 (2009)","journal-title":"J. Optim. Theory Appl."},{"key":"91_CR8","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s10107980013a","volume":"84","author":"BM Glover","year":"1999","unstructured":"Glover, B.M., Jeyakumar, V., Rubinov, A.M.: Dual conditions characterizing optimality for convex multi-objective. Math. Program. 84, 201\u2013217 (1999)","journal-title":"Math. Program."},{"key":"91_CR9","doi-asserted-by":"crossref","unstructured":"van Rooyen, M., Zlobec, X: A saddle point characterization of Pareto optima. Math. Program. 67, 77\u201388 (1994)","DOI":"10.1007\/BF01582213"},{"key":"91_CR10","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1016\/j.jmaa.2005.06.067","volume":"315","author":"RI Bot","year":"2006","unstructured":"Bot, R.I., Wanka, G.: Duality for multiobjective optimization problems with convex objective functions and DC constraints. J. Math. Anal. Appl. 315, 526\u2013543 (2006)","journal-title":"J. Math. Anal. Appl."},{"key":"91_CR11","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1137\/S1052623403424193","volume":"15","author":"JJ Ye","year":"2004","unstructured":"Ye, J.J.: Nondifferentiable multiplier rules for optimization and bileve optimization problems. SIAM J. Optim. 15, 252\u2013274 (2004)","journal-title":"SIAM J. Optim."},{"key":"91_CR12","unstructured":"Caristi, G., Ferrara, M., Stefanescu, A.: Semi-infinite multiobjective programs with generalized invexity, http:\/\/www.csm.ro\/reviste\/Mathematical-Reports\/Pdfs\/2010\/3\/Caristi.pdf"},{"key":"91_CR13","unstructured":"Chen, J.W., Wan, Z.P., Zheng, Y: Optimality conditions and duality for nonsmooth multiobjective optimization problems with cone constraints and applications, http:\/\/www.optimization-online.org\/DBFILE\/2010\/07\/2672.pdf"},{"key":"91_CR14","first-page":"322","volume":"34","author":"L Li","year":"2010","unstructured":"Li, L.: Mond-Weir duality for multiobjective optimization problems with cone constraints. Southeast Asian Bull. Math. 34, 322\u2013332 (2010)","journal-title":"Southeast Asian Bull. Math."},{"key":"91_CR15","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1023\/A:1022606002804","volume":"93","author":"V Jeyakumar","year":"1997","unstructured":"Jeyakumar, V.: Asymptotic dual conditions characterizing optimality for convex programs. J. Optim. Theory Appl. 93, 153\u2013165 (1997)","journal-title":"J. Optim. Theory Appl."},{"key":"91_CR16","first-page":"279","volume":"12","author":"RS Burachik","year":"2005","unstructured":"Burachik, R.S., Jeyakumar, V.: A dual condition for the convex subdifferential sum formula with applications. J. Convex Anal. 12, 279\u2013290 (2005)","journal-title":"J. Convex Anal."},{"key":"91_CR17","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1016\/0022-247X(81)90123-2","volume":"80","author":"MA Hanson","year":"1981","unstructured":"Hanson, M.A.: On the sufficiency of the Kuhn\u2013Tucker conditions. J. Math. Anal. Appl. 80, 545\u2013550 (1981)","journal-title":"J. Math. Anal. Appl."},{"key":"91_CR18","first-page":"1","volume":"5","author":"MA Noor","year":"2004","unstructured":"Noor, M.A.: On generalized preinvex functions and monotonicities. J. Inequal. Pure Appl. Math. 5, 1\u20139 (2004)","journal-title":"J. Inequal. Pure Appl. Math."},{"key":"91_CR19","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/S0022-247X(02)00248-2","volume":"273","author":"XH Chen","year":"2002","unstructured":"Chen, X.H.: Optimization duality theorem for the multiobjective fractional programs with the generalized (F, $$\\rho $$ \u03c1 )-convexity. J. Math. Anal. Appl. 273, 190\u2013205 (2002)","journal-title":"J. Math. Anal. Appl."},{"key":"91_CR20","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1023\/A:1017540412396","volume":"11","author":"L Huang","year":"2001","unstructured":"Huang, L.: Optimality conditions and duality for a class of nonlinear fractional programs. J. Optim. Theory Appl. 11, 611\u2013619 (2001)","journal-title":"J. Optim. Theory Appl."},{"key":"91_CR21","first-page":"779","volume":"32","author":"GJ Zalmai","year":"2008","unstructured":"Zalmai, G.J., Zhang, Q.H.: Semiparametric duality models for semiinfinite multiobjective fractional programs problems containing generalized $$(\\alpha,\\eta,\\rho )$$ ( \u03b1 , \u03b7 , \u03c1 ) -V-invex functions. Southeast Asian Bull. Math. 32, 779\u2013804 (2008)","journal-title":"Southeast Asian Bull. Math."},{"key":"91_CR22","doi-asserted-by":"crossref","unstructured":"Yang, Y: $$F_{\\varepsilon }$$ F \u03b5 -convex function and fractional semi-infinite programming. In: International Conference of Information Science and Management Engineering (2010)","DOI":"10.1109\/ISME.2010.25"}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-013-0091-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-013-0091-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-013-0091-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,20]],"date-time":"2019-07-20T00:30:39Z","timestamp":1563582639000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-013-0091-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7,31]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,5]]}},"alternative-id":["91"],"URL":"https:\/\/doi.org\/10.1007\/s10898-013-0091-9","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,7,31]]}}}