{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T01:09:07Z","timestamp":1778029747193,"version":"3.51.4"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,4,3]],"date-time":"2014-04-03T00:00:00Z","timestamp":1396483200000},"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":[[2015,3]]},"DOI":"10.1007\/s10898-014-0179-x","type":"journal-article","created":{"date-parts":[[2014,4,2]],"date-time":"2014-04-02T22:19:46Z","timestamp":1396477186000},"page":"525-552","source":"Crossref","is-referenced-by-count":67,"title":["Scalarization in set optimization with solid and nonsolid ordering cones"],"prefix":"10.1007","volume":"61","author":[{"given":"C.","family":"Guti\u00e9rrez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"Jim\u00e9nez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E.","family":"Miglierina","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E.","family":"Molho","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,4,3]]},"reference":[{"key":"179_CR1","volume-title":"Infinite Dimensional Analysis. A Hitchhiker\u2019s Guide","author":"CD Aliprantis","year":"2006","unstructured":"Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis. A Hitchhiker\u2019s Guide, 3rd edn. Springer, Berlin (2006)","edition":"3"},{"key":"179_CR2","doi-asserted-by":"crossref","first-page":"3821","DOI":"10.1016\/j.na.2012.02.004","volume":"75","author":"Y Araya","year":"2012","unstructured":"Araya, Y.: Four types of nonlinear scalarizations and some applications in set optimization. Nonlinear Anal. 75, 3821\u20133835 (2012)","journal-title":"Nonlinear Anal."},{"key":"179_CR3","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1111\/1467-9965.00068","volume":"9","author":"P Artzner","year":"1999","unstructured":"Artzner, P., Delbaen, F., Eber, J.-M., Heath, D.: Coherent measures of risk. Math. Finance 9, 203\u2013228 (1999)","journal-title":"Math. Finance"},{"key":"179_CR4","first-page":"109","volume":"4","author":"WW Breckner","year":"1997","unstructured":"Breckner, W.W., Kassay, G.: A systematization of convexity concepts for sets and functions. J. Convex Anal. 4, 109\u2013127 (1997)","journal-title":"J. Convex Anal."},{"key":"179_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-70914-7","volume-title":"Functional Analysis, Sobolev Spaces and Partial Differential Equations","author":"H Brezis","year":"2011","unstructured":"Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, New York (2011)"},{"key":"179_CR6","unstructured":"Chen, G.Y., Huang, X., Yang, X.: Vector optimization. Set-valued and variational analysis. In: Lecture Notes in Economics and Mathematical Systems, vol. 541, Springer, Berlin (2005)"},{"key":"179_CR7","doi-asserted-by":"crossref","unstructured":"Crespi, G.P., Ginchev, I., Rocca, M.: Points of efficiency in vector optimization with increasing-along-rays property and Minty variational inequalities. In: Generalized Convexity and Related Topics. Lecture Notes in Economics and Mathematical Systems, vol. 583, 209\u2013226. Springer, Berlin (2007)","DOI":"10.1007\/978-3-540-37007-9_12"},{"key":"179_CR8","volume-title":"Theory of Value","author":"G Debreu","year":"1959","unstructured":"Debreu, G.: Theory of Value. Wiley, New York (1959)"},{"key":"179_CR9","unstructured":"Gerstewitz (Tammer), Chr.: Nichtkonvexe Dualit\u00e4t in der Vektoroptimierung, Wiss. Zeitschr. Tech. Hochsch. Leuna-Merseburg 25, 357\u2013364 (1983)"},{"key":"179_CR10","unstructured":"Gerth (Tammer), Chr. , Weidner, P.: Nonconvex separation theorems and some applications in vector optimization. J. Optim. Theory Appl. 67, 297\u2013320 (1990)"},{"key":"179_CR11","volume-title":"Variational Methods in Partially Ordered Spaces","author":"A G\u00f6pfert","year":"2003","unstructured":"G\u00f6pfert, A., Rihai, H., Tammer, Chr, Z\u0103linescu, C.: Variational Methods in Partially Ordered Spaces. Springer, Berlin (2003)"},{"key":"179_CR12","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.ejor.2009.02.007","volume":"201","author":"C Guti\u00e9rrez","year":"2010","unstructured":"Guti\u00e9rrez, C., Jim\u00e9nez, B., Novo, V.: Optimality conditions via scalarization for a new $$\\varepsilon $$ \u03b5 -efficiency concept in vector optimization problems. Eur. J. Oper. Res. 201, 11\u201322 (2010)","journal-title":"Eur. J. Oper. Res."},{"key":"179_CR13","doi-asserted-by":"crossref","first-page":"3842","DOI":"10.1016\/j.na.2010.08.012","volume":"73","author":"C Guti\u00e9rrez","year":"2010","unstructured":"Guti\u00e9rrez, C., Jim\u00e9nez, B., Novo, V., Thibault, L.: Strict approximate solutions in set-valued optimization with applications to the approximate Ekeland variational principle. Nonlinear Anal. 73, 3842\u20133855 (2010)","journal-title":"Nonlinear Anal."},{"key":"179_CR14","doi-asserted-by":"crossref","first-page":"1822","DOI":"10.1016\/j.na.2011.09.028","volume":"75","author":"C Guti\u00e9rrez","year":"2012","unstructured":"Guti\u00e9rrez, C., Miglierina, E., Molho, E., Novo, V.: Pointwise well-posedness in set optimization with cone proper sets. Nonlinear Anal. 75, 1822\u20131833 (2012)","journal-title":"Nonlinear Anal."},{"key":"179_CR15","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/s10957-004-6472-y","volume":"124","author":"TXD Ha","year":"2005","unstructured":"Ha, T.X.D.: Some variants of the Ekeland variational principle for a set-valued map. J. Optim. Theory Appl. 124, 187\u2013206 (2005)","journal-title":"J. Optim. Theory Appl."},{"key":"179_CR16","unstructured":"Hamel, A.: Translative sets and functions and their applications to risk measure theory and nonlinear separation, IMPA Preprint Series D 21 (2006)"},{"key":"179_CR17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11579-011-0047-0","volume":"5","author":"A Hamel","year":"2011","unstructured":"Hamel, A., Heyde, F., Rudloff, B.: Set-valued risk measures for conical market models. Math. Financ. Econ. 5, 1\u201328 (2011)","journal-title":"Math. Financ. Econ."},{"key":"179_CR18","first-page":"19","volume":"7","author":"A Hamel","year":"2006","unstructured":"Hamel, A., L\u00f6hne, A.: Minimal element theorems and Ekeland\u2019s principle with set relations. J. Nonlinear Convex Anal. 7, 19\u201337 (2006)","journal-title":"J. Nonlinear Convex Anal."},{"key":"179_CR19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jmaa.2006.01.033","volume":"325","author":"E Hern\u00e1ndez","year":"2007","unstructured":"Hern\u00e1ndez, E., Rodr\u00edguez-Mar\u00edn, L.: Nonconvex scalarization in set optimization with set-valued maps. J. Math. Anal. Appl. 325, 1\u201318 (2007)","journal-title":"J. Math. Anal. Appl."},{"key":"179_CR20","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1287\/moor.4.1.79","volume":"4","author":"J-B Hiriart-Urruty","year":"1979","unstructured":"Hiriart-Urruty, J.-B.: Tangent cones, generalized gradients and mathematical programming in Banach spaces. Math. Oper. Res. 4, 79\u201397 (1979)","journal-title":"Math. Oper. Res."},{"key":"179_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-17005-8","volume-title":"Vector Optimization. Theory, Applications and Extensions","author":"J Jahn","year":"2011","unstructured":"Jahn, J.: Vector Optimization. Theory, Applications and Extensions, 2nd edn. Springer, Berlin (2011)","edition":"2"},{"key":"179_CR22","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s10957-010-9752-8","volume":"148","author":"J Jahn","year":"2011","unstructured":"Jahn, J., Ha, T.X.D.: New order relations in set optimization. J. Optim. Theory Appl. 148, 209\u2013236 (2011)","journal-title":"J. Optim. Theory Appl."},{"key":"179_CR23","unstructured":"Kuroiwa, D.: Some duality theorems of set-valued optimization with natural criteria. In: Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis, pp. 221\u2013228. World Scientific, River Edge (1999)"},{"key":"179_CR24","doi-asserted-by":"crossref","first-page":"1395","DOI":"10.1016\/S0362-546X(01)00274-7","volume":"47","author":"D Kuroiwa","year":"2001","unstructured":"Kuroiwa, D.: On set-valued optimization. Nonlinear Anal. 47, 1395\u20131400 (2001)","journal-title":"Nonlinear Anal."},{"key":"179_CR25","doi-asserted-by":"crossref","first-page":"1487","DOI":"10.1016\/S0362-546X(97)00213-7","volume":"30","author":"D Kuroiwa","year":"1997","unstructured":"Kuroiwa, D., Tanaka, T., Ha, T.X.D.: On cone convexity of set-valued maps. Nonlinear Anal. 30, 1487\u20131496 (1997)","journal-title":"Nonlinear Anal."},{"key":"179_CR26","first-page":"193","volume-title":"Nonlinear Analysis and Optimization","author":"I Kuwano","year":"2009","unstructured":"Kuwano, I., Tanaka, T., Yamada, S.: Characterization of nonlinear scalarizing functions for set-valued maps. In: Akashi, S., Takahashi, W., Tanaka, T. (eds.) Nonlinear Analysis and Optimization, pp. 193\u2013204. Yokohama Publishers, Yokohama (2009)"},{"key":"179_CR27","first-page":"513","volume":"11","author":"I Kuwano","year":"2010","unstructured":"Kuwano, I., Tanaka, T., Yamada, S.: Unified scalarization for sets and set-valued Ky Fan minimax inequality. J. Nonlinear Convex Anal. 11, 513\u2013525 (2010)","journal-title":"J. Nonlinear Convex Anal."},{"key":"179_CR28","unstructured":"Kuwano, I., Tanaka, T., Yamada, S.: Inherited properties of nonlinear scalarizing functions for set-valued maps. In: Akashi, S., Kimura, Y., Tanaka, T. (eds.) Nonlinear Analysis and Convex Analysis, pp. 161\u2013177, Yokohama Publishers, Yokohama (2010)"},{"key":"179_CR29","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-50280-4","volume-title":"Theory of Vector Optimization","author":"DT Luc","year":"1989","unstructured":"Luc, D.T.: Theory of Vector Optimization. Springer, Berlin (1989)"},{"key":"179_CR30","doi-asserted-by":"crossref","DOI":"10.1007\/0-387-31082-7","volume-title":"Convexity and Well-Posed Problems","author":"R Lucchetti","year":"2006","unstructured":"Lucchetti, R.: Convexity and Well-Posed Problems. Springer, New York (2006)"},{"key":"179_CR31","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s10957-011-9952-x","volume":"153","author":"T Maeda","year":"2012","unstructured":"Maeda, T.: On optimization problems with set-valued objective maps: existence and optimality. J. Optim. Theory Appl. 153, 263\u2013279 (2012)","journal-title":"J. Optim. Theory Appl."},{"key":"179_CR32","volume-title":"Nonlinear Multiobjective Optimization","author":"KM Miettinen","year":"1999","unstructured":"Miettinen, K.M.: Nonlinear Multiobjective Optimization. Kluwer, Boston (1999)"},{"key":"179_CR33","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1023\/A:1016031214488","volume":"114","author":"E Miglierina","year":"2002","unstructured":"Miglierina, E., Molho, E.: Scalarization and stability in vector optimization. J. Optim. Theory Appl. 114, 657\u2013670 (2002)","journal-title":"J. Optim. Theory Appl."},{"key":"179_CR34","doi-asserted-by":"crossref","first-page":"93","DOI":"10.2307\/1909243","volume":"38","author":"B Peleg","year":"1970","unstructured":"Peleg, B.: Utility functions for partially ordered topological spaces. Econometrica 38, 93\u201396 (1970)","journal-title":"Econometrica"},{"key":"179_CR35","doi-asserted-by":"crossref","first-page":"635","DOI":"10.2307\/1909773","volume":"34","author":"M Richter","year":"1966","unstructured":"Richter, M.: Revealed preference theory. Econometrica 34, 635\u2013645 (1966)","journal-title":"Econometrica"},{"key":"179_CR36","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1080\/02331930108844567","volume":"50","author":"A Rubinov","year":"2001","unstructured":"Rubinov, A., Singer, I.: Topical and sub-topical functions, downward sets and abstract convexity. Optimization 50, 307\u2013351 (2001)","journal-title":"Optimization"},{"key":"179_CR37","unstructured":"Shimizu, A., Nishizawa, S., Tanaka, T.: Optimality conditions in set-valued optimization using nonlinear scalarization methods. In: Proceedings of the 4th International Conference on Nonlinear Analysis and Convex Analysis (Okinawa, 2005), pp. 565\u2013574. Yokohama Publishers, Yokohama (2007)"},{"key":"179_CR38","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/BF01719738","volume":"8","author":"AP Wierzbicki","year":"1986","unstructured":"Wierzbicki, A.P.: On the completeness and constructiveness of parametric characterizations to vector optimization problems. OR Spectrum 8, 73\u201387 (1986)","journal-title":"OR Spectrum"},{"key":"179_CR39","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1137\/S0363012902411532","volume":"42","author":"A Zaffaroni","year":"2003","unstructured":"Zaffaroni, A.: Degrees of efficiency and degrees of minimality. SIAM J. Control Optim. 42, 1071\u20131086 (2003)","journal-title":"SIAM J. Control Optim."},{"key":"179_CR40","doi-asserted-by":"crossref","first-page":"3769","DOI":"10.1016\/j.na.2009.02.036","volume":"71","author":"WY Zhang","year":"2009","unstructured":"Zhang, W.Y., Li, S.J., Teo, K.L.: Well-posedness for set optimization problems. Nonlinear Anal. 71, 3769\u20133778 (2009)","journal-title":"Nonlinear Anal."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-014-0179-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-014-0179-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-014-0179-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T19:12:22Z","timestamp":1689102742000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-014-0179-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4,3]]},"references-count":40,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,3]]}},"alternative-id":["179"],"URL":"https:\/\/doi.org\/10.1007\/s10898-014-0179-x","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,4,3]]}}}