{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T13:15:27Z","timestamp":1762866927709},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,8,16]],"date-time":"2016-08-16T00:00:00Z","timestamp":1471305600000},"content-version":"unspecified","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":[[2016,12]]},"DOI":"10.1007\/s10957-016-0992-0","type":"journal-article","created":{"date-parts":[[2016,8,16]],"date-time":"2016-08-16T16:10:49Z","timestamp":1471363849000},"page":"931-946","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":25,"title":["Set Approach for Set Optimization with Variable Ordering Structures Part I: Set Relations and Relationship to Vector Approach"],"prefix":"10.1007","volume":"171","author":[{"given":"Gabriele","family":"Eichfelder","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maria","family":"Pilecka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,8,16]]},"reference":[{"key":"992_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-24828-6","volume-title":"Vector Optimization","author":"J Jahn","year":"2004","unstructured":"Jahn, J.: Vector Optimization. Springer, Berlin (2004)"},{"key":"992_CR2","volume-title":"Foundations of Bilevel Programming","author":"S Dempe","year":"2002","unstructured":"Dempe, S.: Foundations of Bilevel Programming. Kluwer Academic Publishers, Dordrecht (2002)"},{"key":"992_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-54265-7","volume-title":"Set-valued Optimization\u2014an Introduction with Applications","author":"A Khan","year":"2015","unstructured":"Khan, A., Tammer, C., Z\u01celinescu, C.: Set-valued Optimization\u2014an Introduction with Applications. Springer, Heidelberg (2015)"},{"key":"992_CR4","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1007\/s10898-014-0207-x","volume":"61","author":"M Durea","year":"2015","unstructured":"Durea, M., Strugariu, R., Tammer, C.: On set-valued optimization problems with variable ordering structure. J. Glob. Optim. 61, 745\u2013767 (2015)","journal-title":"J. Glob. Optim."},{"key":"992_CR5","doi-asserted-by":"crossref","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 for multiobjective problems: existence and optimality conditions. Math. Progr. Ser. A 122, 301\u2013347 (2010)","journal-title":"Math. Progr. Ser. A"},{"key":"992_CR6","doi-asserted-by":"crossref","unstructured":"Luc, D.T.: Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems, vol. 319. Springer, Berlin (1989)","DOI":"10.1007\/978-3-642-50280-4"},{"key":"992_CR7","volume-title":"Recent Developments in Vector Optimization","author":"G Eichfelder","year":"2012","unstructured":"Eichfelder, G., Jahn, J.: Vector optimization problems and their solution concepts. In: Ansari, Q.H., Yao, J.-C. (eds.) Recent Developments in Vector Optimization. Springer, Berlin (2012)"},{"key":"992_CR8","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":"992_CR9","first-page":"85","volume":"1031","author":"D Kuroiwa","year":"1998","unstructured":"Kuroiwa, D.: The natural criteria in set-valued optimization. RIMS Kokyuroku 1031, 85\u201390 (1998)","journal-title":"RIMS Kokyuroku"},{"key":"992_CR10","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1080\/02331938008842630","volume":"11","author":"JW Nieuwenhuis","year":"1980","unstructured":"Nieuwenhuis, J.W.: Supremal points and generalized duality. Math. Operationsforsch. Statist. Ser. Optim. 11, 41\u201359 (1980)","journal-title":"Math. Operationsforsch. Statist. Ser. Optim."},{"key":"992_CR11","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1016\/0022-247X(88)90314-9","volume":"130","author":"T Tanino","year":"1988","unstructured":"Tanino, T.: On supremum of a set in a multi-dimensional space. J. Math. Anal. Appl. 130, 386\u2013397 (1988)","journal-title":"J. Math. Anal. Appl."},{"key":"992_CR12","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1007\/s10957-013-0332-6","volume":"162","author":"TQ Bao","year":"2014","unstructured":"Bao, T.Q., Mordukhovich, B.S.: Necessary nondomination conditions in set and vector optimization with variable ordering structures. J. Optim. Theory Appl. 162, 350\u2013370 (2014)","journal-title":"J. Optim. Theory Appl."},{"key":"992_CR13","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/s10957-013-0308-6","volume":"162","author":"JYB Cruz","year":"2014","unstructured":"Cruz, J.Y.B., Allende, G.B.: A steepest descent-like method for variable order vector optimization problems. J. Optim. Theory Appl. 162, 371\u2013391 (2014)","journal-title":"J. Optim. Theory Appl."},{"key":"992_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-54283-1","volume-title":"Variable Ordering Structures in Vector Optimization","author":"G Eichfelder","year":"2014","unstructured":"Eichfelder, G.: Variable Ordering Structures in Vector Optimization. Springer, Heidelberg (2014)"},{"key":"992_CR15","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/s10898-007-9246-x","volume":"42","author":"A Engau","year":"2008","unstructured":"Engau, A.: Variable preference modeling with ideal-symmetric convex cones. J. Glob. Optim. 42, 295\u2013311 (2008)","journal-title":"J. Glob. Optim."},{"key":"992_CR16","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.jmateco.2013.05.004","volume":"49","author":"DT Luc","year":"2013","unstructured":"Luc, D.T., Soubeyran, A.: Variable preference relations: existence of maximal elements. J. Math. Econom. 49, 251\u2013262 (2013)","journal-title":"J. Math. Econom."},{"key":"992_CR17","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1007\/s10957-014-0535-5","volume":"162","author":"S Soleimani","year":"2014","unstructured":"Soleimani, S.: Characterization of approximate solutions of vector optimization problems with a variable order structure. J. Optim. Theory Appl. 162, 605\u2013632 (2014)","journal-title":"J. Optim. Theory Appl."},{"key":"992_CR18","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1080\/02331934.2011.575939","volume":"62","author":"G Eichfelder","year":"2013","unstructured":"Eichfelder, G., Ha, T.X.D.: Optimality conditions for vector optimization problems with variable ordering structures. Optimization 62, 597\u2013627 (2013)","journal-title":"Optimization"},{"key":"992_CR19","doi-asserted-by":"publisher","unstructured":"K\u00f6bis, E.: Set optimization by means of variable order relations. Optimization (2016). doi: 10.1080\/02331934.2016.1172226","DOI":"10.1080\/02331934.2016.1172226"},{"key":"992_CR20","doi-asserted-by":"publisher","unstructured":"Eichfelder, G., Pilecka, M.: Set approach for set optimization with variable ordering structures part II: scalarization approaches. J. Optim. Theory Appl. (2016). doi: 10.1007\/s10957-016-0993-z","DOI":"10.1007\/s10957-016-0993-z"},{"key":"992_CR21","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":"992_CR22","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.1016\/j.camwa.2010.06.022","volume":"60","author":"E Hern\u00e1ndez","year":"2010","unstructured":"Hern\u00e1ndez, E., Rodr\u00edguez-Mar\u00edn, L., Sama, M.: On solutions of set-valued optimization problems. Comput. Math. Appl. 60, 1401\u20131408 (2010)","journal-title":"Comput. Math. Appl."},{"key":"992_CR23","first-page":"41","volume":"10","author":"D Kuroiwa","year":"2009","unstructured":"Kuroiwa, D.: On derivatives of set-valued maps and optimality conditions for set optimization. J. Nonlinear Convex Anal. 10, 41\u201350 (2009)","journal-title":"J. Nonlinear Convex Anal."},{"key":"992_CR24","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":"992_CR25","unstructured":"Chiriaev, D., Walster, G.W.: Interval arithmetic specification. Technical Report (1998)"},{"key":"992_CR26","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-18351-5","volume-title":"Vector Optimization with Infimum and Supremum","author":"A L\u00f6hne","year":"2011","unstructured":"L\u00f6hne, A.: Vector Optimization with Infimum and Supremum. Springer, Berlin Heidelberg (2011)"},{"key":"992_CR27","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1007\/s10957-013-0363-z","volume":"167","author":"J Jahn","year":"2015","unstructured":"Jahn, J.: Vectorization in set optimization. J. Optim. Theory Appl. 167, 783\u2013795 (2015)","journal-title":"J. Optim. Theory Appl."},{"key":"992_CR28","doi-asserted-by":"crossref","first-page":"974","DOI":"10.1016\/j.jmaa.2007.01.105","volume":"335","author":"L Rodr\u00edguez-Mar\u00edn","year":"2007","unstructured":"Rodr\u00edguez-Mar\u00edn, L., Sama, M.: $$(\\Lambda, C)$$ ( \u039b , C ) -contingent derivatives of set-valued maps. J. Math. Anal. Appl. 335, 974\u2013989 (2007)","journal-title":"J. Math. Anal. Appl."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-016-0992-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-016-0992-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-016-0992-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,19]],"date-time":"2023-08-19T18:00:18Z","timestamp":1692468018000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-016-0992-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,16]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,12]]}},"alternative-id":["992"],"URL":"https:\/\/doi.org\/10.1007\/s10957-016-0992-0","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,8,16]]}}}