{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T11:08:36Z","timestamp":1759230516454,"version":"3.37.3"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T00:00:00Z","timestamp":1565654400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T00:00:00Z","timestamp":1565654400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2019,11,1]]},"DOI":"10.1007\/s10957-019-01577-w","type":"journal-article","created":{"date-parts":[[2019,8,13]],"date-time":"2019-08-13T11:04:39Z","timestamp":1565694279000},"page":"471-489","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Optimality and Duality in Nonsmooth Conic Vector Optimization"],"prefix":"10.1007","volume":"183","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0893-5604","authenticated-orcid":false,"given":"Thai Doan","family":"Chuong","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,8,13]]},"reference":[{"key":"1577_CR1","volume-title":"Vector Optimization. Theory, Applications, and Extensions","author":"J Jahn","year":"2004","unstructured":"Jahn, J.: Vector Optimization. Theory, Applications, and Extensions. Springer, Berlin (2004)"},{"key":"1577_CR2","volume-title":"Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems","author":"DT Luc","year":"1989","unstructured":"Luc, D.T.: Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems, vol. 319. Springer, Berlin (1989)"},{"key":"1577_CR3","doi-asserted-by":"publisher","first-page":"1269","DOI":"10.1080\/02331934.2010.505959","volume":"60","author":"RI Bot","year":"2011","unstructured":"Bot, R.I., Grad, S.-M.: Duality for vector optimization problems via a general scalarization. Optimization 60, 1269\u20131290 (2011)","journal-title":"Optimization"},{"key":"1577_CR4","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/s10957-009-9551-2","volume":"143","author":"I Ginchev","year":"2009","unstructured":"Ginchev, I., Guerraggio, A., Rocca, M.: Dini set-valued directional derivative in locally Lipschitz vector optimization. J. Optim. Theory Appl. 143, 87\u2013105 (2009)","journal-title":"J. Optim. Theory Appl."},{"key":"1577_CR5","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1080\/02331930601120516","volume":"57","author":"B Jimenez","year":"2008","unstructured":"Jimenez, B., Novo, V.: First order optimality conditions in vector optimization involving stable functions. Optimization 57, 449\u2013471 (2008)","journal-title":"Optimization"},{"key":"1577_CR6","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173","volume-title":"Convex Analysis","author":"RT Rockafellar","year":"1970","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)"},{"key":"1577_CR7","volume-title":"Optimization and Nonsmooth Analysis","author":"FH Clarke","year":"1983","unstructured":"Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)"},{"key":"1577_CR8","doi-asserted-by":"publisher","first-page":"3107","DOI":"10.1016\/j.na.2011.12.009","volume":"75","author":"T Antczak","year":"2012","unstructured":"Antczak, T.: Proper efficiency conditions and duality results for nonsmooth vector optimization in Banach spaces under $$(\\Phi,\\rho )$$-invexity. Nonlinear Anal. 75, 3107\u20133121 (2012)","journal-title":"Nonlinear Anal."},{"key":"1577_CR9","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1023\/A:1021769232224","volume":"103","author":"AJV Brandao","year":"1999","unstructured":"Brandao, A.J.V., Rojas-Medar, M.A., Silva, G.N.: Optimality conditions for Pareto nonsmooth nonconvex programming in Banach spaces. J. Optim. Theory Appl. 103, 65\u201373 (1999)","journal-title":"J. Optim. Theory Appl."},{"key":"1577_CR10","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/s10898-010-9539-3","volume":"49","author":"JW Chen","year":"2011","unstructured":"Chen, J.W., Cho, Y.J., Kim, J.K., Li, J.: Multiobjective optimization problems with modified objective functions and cone constraints and applications. J. Global Optim. 49, 137\u2013147 (2011)","journal-title":"J. Global Optim."},{"key":"1577_CR11","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.jmaa.2006.12.047","volume":"334","author":"C Fulga","year":"2007","unstructured":"Fulga, C., Preda, V.: On optimality conditions for multiobjective optimization problems in topological vector space. J. Math. Anal. Appl. 334, 123\u2013131 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"1577_CR12","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/S0022-247X(03)00106-9","volume":"290","author":"Y Hu","year":"2004","unstructured":"Hu, Y., Ling, C.: The generalized optimality conditions of multiobjective programming problem in topological vector space. J. Math. Anal. Appl. 290, 363\u2013372 (2004)","journal-title":"J. Math. Anal. Appl."},{"key":"1577_CR13","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1080\/02331930108844561","volume":"50","author":"M Pappalardo","year":"2001","unstructured":"Pappalardo, M., Stocklin, W.: Necessary optimality conditions in nondifferentiable vector optimization. Optimization 50, 233\u2013251 (2001)","journal-title":"Optimization"},{"key":"1577_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-31246-3","volume-title":"Variational Analysis and Generalized Differentiation. I: Basic Theory","author":"BS Mordukhovich","year":"2006","unstructured":"Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation. I: Basic Theory. Springer, Berlin (2006)"},{"key":"1577_CR15","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/s10479-014-1552-3","volume":"217","author":"TD Chuong","year":"2014","unstructured":"Chuong, T.D., Kim, D.S.: Optimality conditions and duality in nonsmooth multiobjective optimization problems. Ann. Oper. Res. 217, 117\u2013136 (2014)","journal-title":"Ann. Oper. Res."},{"key":"1577_CR16","doi-asserted-by":"publisher","first-page":"748","DOI":"10.1007\/s10957-013-0314-8","volume":"160","author":"TD Chuong","year":"2014","unstructured":"Chuong, T.D., Kim, D.S.: Nonsmooth semi-infinite multiobjective optimization problems. J. Optim. Theory Appl. 160, 748\u2013762 (2014)","journal-title":"J. Optim. Theory Appl."},{"key":"1577_CR17","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1137\/S1052623402414701","volume":"14","author":"BS Mordukhovich","year":"2003","unstructured":"Mordukhovich, B.S., Treiman, J.S., Zhu, Q.J.: An extended extremal principle with applications to set-valued optimization. SIAM J. Optim. 14, 359\u2013379 (2003)","journal-title":"SIAM J. Optim."},{"key":"1577_CR18","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1007\/s10898-008-9336-4","volume":"43","author":"TQ Bao","year":"2009","unstructured":"Bao, T.Q., Mordukhovich, B.S.: Necessary conditions for super minimizers in constrained multiobjective optimization. J. Global Optim. 43, 533\u2013552 (2009)","journal-title":"J. Global Optim."},{"key":"1577_CR19","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/s10107-008-0249-2","volume":"122","author":"TQ Bao","year":"2010","unstructured":"Bao, T.Q., Mordukhovich, B.S.: Relative Pareto minimizers in multiobjective optimization: existence and optimality conditions. Math. Program. 122, 301\u2013347 (2010)","journal-title":"Math. Program."},{"key":"1577_CR20","doi-asserted-by":"publisher","first-page":"2466","DOI":"10.1137\/17M1143484","volume":"28","author":"TD Chuong","year":"2018","unstructured":"Chuong, T.D.: Linear matrix inequality conditions and duality for a class of robust multiobjective convex polynomial programs. SIAM J. Optim. 28, 2466\u20132488 (2018)","journal-title":"SIAM J. Optim."},{"key":"1577_CR21","doi-asserted-by":"publisher","first-page":"685","DOI":"10.1080\/02331930600816395","volume":"55","author":"BS Mordukhovich","year":"2006","unstructured":"Mordukhovich, B.S., Nam, N.M., Yen, N.D.: Fr\u00e9chet subdifferential calculus and optimality conditions in nondifferentiable programming. Optimization 55, 685\u2013708 (2006)","journal-title":"Optimization"},{"key":"1577_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-92775-6","volume-title":"Variational Analysis and Applications","author":"BS Mordukhovich","year":"2018","unstructured":"Mordukhovich, B.S.: Variational Analysis and Applications. Springer, Cham (2018)"},{"key":"1577_CR23","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1287\/moor.2013.0622","volume":"39","author":"BS Mordukhovich","year":"2014","unstructured":"Mordukhovich, B.S., Nghia, T.T.A.: Nonsmooth cone-constrained optimization with applications to semi-infinite programming. Math. Oper. Res. 39, 301\u2013324 (2014)","journal-title":"Math. Oper. Res."},{"key":"1577_CR24","doi-asserted-by":"publisher","first-page":"534","DOI":"10.1137\/S1052623402417699","volume":"14","author":"V Jeyakumar","year":"2003","unstructured":"Jeyakumar, V., Lee, G.M., Dinh, N.: New sequential Lagrange multiplier conditions characterizing optimality without constraint qualification for convex programs. SIAM J. Optim. 14, 534\u2013547 (2003)","journal-title":"SIAM J. Optim."},{"key":"1577_CR25","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1016\/j.jmaa.2007.12.066","volume":"342","author":"RI Bot","year":"2008","unstructured":"Bot, R.I., Csetnek, E.R., Wanka, G.: Sequential optimality conditions for composed convex optimization problems. J. Math. Anal. Appl. 342, 1015\u20131025 (2008)","journal-title":"J. Math. Anal. Appl."},{"key":"1577_CR26","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1090\/qam\/135625","volume":"19","author":"P Wolfe","year":"1961","unstructured":"Wolfe, P.: A duality theorem for nonlinear programming. Quart. Appl. Math. 19, 239\u2013244 (1961)","journal-title":"Quart. Appl. Math."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-019-01577-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-019-01577-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-019-01577-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,11]],"date-time":"2020-08-11T23:44:44Z","timestamp":1597189484000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-019-01577-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,13]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,11,1]]}},"alternative-id":["1577"],"URL":"https:\/\/doi.org\/10.1007\/s10957-019-01577-w","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"type":"print","value":"0022-3239"},{"type":"electronic","value":"1573-2878"}],"subject":[],"published":{"date-parts":[[2019,8,13]]},"assertion":[{"value":"26 December 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 August 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 August 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}