{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T19:36:52Z","timestamp":1773517012168,"version":"3.50.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2012,4,3]],"date-time":"2012-04-03T00:00:00Z","timestamp":1333411200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2012,9]]},"DOI":"10.1007\/s10957-012-0045-2","type":"journal-article","created":{"date-parts":[[2012,4,2]],"date-time":"2012-04-02T16:15:25Z","timestamp":1333383325000},"page":"830-841","source":"Crossref","is-referenced-by-count":17,"title":["Scalarization of Set-Valued Optimization Problems with Generalized Cone Subconvexlikeness in Real Ordered Linear Spaces"],"prefix":"10.1007","volume":"154","author":[{"given":"Z. A.","family":"Zhou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. W.","family":"Peng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,4,3]]},"reference":[{"key":"45_CR1","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s001860050026","volume":"48","author":"W.D. Rong","year":"1998","unstructured":"Rong, W.D., Wu, Y.N.: Characterizations of super efficiency in cone-convexlike vector optimization with set-valued maps. Math. Methods Oper. Res. 48, 247\u2013258 (1998)","journal-title":"Math. Methods Oper. Res."},{"key":"45_CR2","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1023\/A:1021786303883","volume":"100","author":"Z.M. Li","year":"1999","unstructured":"Li, Z.M.: A theorem of the alternative and its application to the optimization of set-valued maps. J.\u00a0Optim. Theory Appl. 100, 365\u2013375 (1999)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"45_CR3","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1023\/A:1022658019642","volume":"93","author":"W. Song","year":"1997","unstructured":"Song, W.: Lagrangian duality for minimization of nonconvex multifunctions. J.\u00a0Optim. Theory Appl. 93, 167\u2013182 (1997)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"45_CR4","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1023\/A:1026407517917","volume":"107","author":"X.M. Yang","year":"2000","unstructured":"Yang, X.M., Yang, X.Q., Chen, G.Y.: Theorems of the alternative and optimization with set-valued maps. J.\u00a0Optim. Theory Appl. 107, 627\u2013640 (2000)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"45_CR5","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1023\/A:1017535631418","volume":"110","author":"X.M. Yang","year":"2001","unstructured":"Yang, X.M., Li, D., Wang, S.Y.: Near-subconvexlikeness in vector optimization with set-valued functions. J.\u00a0Optim. Theory Appl. 110, 413\u2013427 (2001)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"45_CR6","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s10957-004-1716-4","volume":"125","author":"P.H. Sach","year":"2005","unstructured":"Sach, P.H.: New generalized convexity notion for set-valued maps and application to vector optimization. J.\u00a0Optim. Theory Appl. 125, 157\u2013179 (2005)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"45_CR7","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1006\/jmaa.1999.6426","volume":"237","author":"Z.M. Li","year":"1999","unstructured":"Li, Z.M.: The optimality conditions for vector optimization of set-valued maps. J.\u00a0Math. Anal. Appl. 237, 413\u2013424 (1999)","journal-title":"J.\u00a0Math. Anal. Appl."},{"issue":"2","key":"45_CR8","first-page":"275","volume":"14","author":"M. Ad\u00e1n","year":"2007","unstructured":"Ad\u00e1n, M., Novo, V.: Weak and proper efficiency in set-valued optimization on real linear spaces. J.\u00a0Convex Anal. 14(2), 275\u2013296 (2007)","journal-title":"J.\u00a0Convex Anal."},{"key":"45_CR9","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1023\/A:1022676013609","volume":"98","author":"Z.F. Li","year":"1998","unstructured":"Li, Z.F.: Benson proper efficiency in the vector optimization of set-valued maps. J.\u00a0Optim. Theory Appl. 98, 623\u2013649 (1998)","journal-title":"J.\u00a0Optim. Theory Appl."},{"issue":"11","key":"45_CR10","doi-asserted-by":"crossref","first-page":"1921","DOI":"10.1007\/s10114-009-6144-9","volume":"25","author":"G.L. Yu","year":"2009","unstructured":"Yu, G.L., Liu, S.Y.: Globally proper saddle point in ic-cone-convexlike set-valued optimization problems. Acta Math. Sin. 25(11), 1921\u20131928 (2009)","journal-title":"Acta Math. Sin."},{"key":"45_CR11","volume-title":"Convex Analysis","author":"J.V. Tiel","year":"1984","unstructured":"Tiel, J.V.: Convex Analysis. Wiley, New York (1984)"},{"key":"45_CR12","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1016\/S0377-2217(02)00444-7","volume":"149","author":"M. Ad\u00e1n","year":"2003","unstructured":"Ad\u00e1n, M., Novo, V.: Weak efficiency in vector optimization using a closure of algebraic type under cone-convexlikeness. Eur. J. Oper. Res. 149, 641\u2013653 (2003)","journal-title":"Eur. J. Oper. Res."},{"key":"45_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-17005-8","volume-title":"Vector Optimization\u2014Theory, Applications and Extensions","author":"J. Jahn","year":"2011","unstructured":"Jahn, J.: Vector Optimization\u2014Theory, Applications and Extensions, 2nd edn. Springer, Berlin (2011)","edition":"2"},{"key":"45_CR14","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BF02592221","volume":"29","author":"J. Jahn","year":"1984","unstructured":"Jahn, J.: Scalarization in vector optimization. Math. Program. 29, 203\u2013218 (1984)","journal-title":"Math. Program."},{"key":"45_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02191776","volume":"82","author":"A. Guerraggio","year":"1994","unstructured":"Guerraggio, A., Molho, E., Zaffaroni, A.: On the notion of proper efficiency in vector optimization. J.\u00a0Optim. Theory Appl. 82, 1\u201321 (1994)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"45_CR16","first-page":"63","volume":"5","author":"Y.W. Huang","year":"2001","unstructured":"Huang, Y.W., Li, Z.M.: Optimality condition and Lagrangian multipliers of vector optimization with set-valued maps in linear spaces. Oper. Res. Trans. 5, 63\u201369 (2001)","journal-title":"Oper. Res. Trans."},{"key":"45_CR17","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1023\/A:1004657412928","volume":"106","author":"W.D. Rong","year":"2000","unstructured":"Rong, W.D., Wu, Y.N.: \u03f5-Weak minimal solutions of vector optimization problems with set-valued maps. J.\u00a0Optim. Theory Appl. 106, 569\u2013579 (2000)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"45_CR18","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1007\/s11741-010-0662-3","volume":"14","author":"Z.A. Zhou","year":"2010","unstructured":"Zhou, Z.A.: Benson proper efficiency for vector optimization of generalized subconvexlike set-valued maps in ordered linear spaces. J.\u00a0Shanghai Univ. 14, 374\u2013379 (2010)","journal-title":"J.\u00a0Shanghai Univ."},{"key":"45_CR19","first-page":"398","volume":"25","author":"L.G. Huang","year":"2005","unstructured":"Huang, L.G., Liu, S.Y.: Saddle points and Lagrangian dual problems of vector-valued map. J.\u00a0Syst. Sci. Math. Sci. 25, 398\u2013405 (2005)","journal-title":"J.\u00a0Syst. Sci. Math. Sci."},{"key":"45_CR20","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/BF02191762","volume":"83","author":"Z.F. Li","year":"1994","unstructured":"Li, Z.F., Wang, S.Y.: Lagrange multipliers and saddle points in multiobjective programming. J.\u00a0Optim. Theory Appl. 83, 63\u201381 (1994)","journal-title":"J.\u00a0Optim. Theory Appl."},{"key":"45_CR21","doi-asserted-by":"crossref","unstructured":"Chinaie, M., Zafarani, J.: Image space analysis and scalarization for \u03f5-optimization of multifunctions. J. Optim. Theory Appl. doi: 10.1007\/s10957-010-9657-6","DOI":"10.1007\/s10957-010-9657-6"},{"key":"45_CR22","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1023\/B:JOTA.0000037602.13941.ed","volume":"121","author":"M. Ad\u00e1n","year":"2004","unstructured":"Ad\u00e1n, M., Novo, V.: Proper efficiency in vector optimization on real linear spaces. J.\u00a0Optim. Theory Appl. 121, 515\u2013540 (2004)","journal-title":"J.\u00a0Optim. Theory Appl."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-012-0045-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-012-0045-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-012-0045-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,22]],"date-time":"2024-04-22T15:54:48Z","timestamp":1713801288000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-012-0045-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,4,3]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,9]]}},"alternative-id":["45"],"URL":"https:\/\/doi.org\/10.1007\/s10957-012-0045-2","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,4,3]]}}}