{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T19:09:13Z","timestamp":1775070553389,"version":"3.50.1"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2013,12,28]],"date-time":"2013-12-28T00:00:00Z","timestamp":1388188800000},"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":[[2014,12]]},"DOI":"10.1007\/s10898-013-0132-4","type":"journal-article","created":{"date-parts":[[2013,12,27]],"date-time":"2013-12-27T19:51:18Z","timestamp":1388173878000},"page":"689-712","source":"Crossref","is-referenced-by-count":35,"title":["Properly optimal elements in vector optimization with variable ordering structures"],"prefix":"10.1007","volume":"60","author":[{"given":"Gabriele","family":"Eichfelder","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Refail","family":"Kasimbeyli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,12,28]]},"reference":[{"key":"132_CR1","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.camwa.2006.08.014","volume":"52","author":"D Baatar","year":"2006","unstructured":"Baatar, D., Wiecek, M.M.: Advancing equitability in multiobjective programming. Comput. Math. Appl. 52, 225\u2013234 (2006)","journal-title":"Comput. Math. Appl."},{"key":"132_CR2","first-page":"232","volume":"71","author":"HP Benson","year":"1979","unstructured":"Benson, H.P.: An improved definition of proper efficiency for vector maximization with respect to cones. J. Math. Appl. 71, 232\u2013241 (1979)","journal-title":"J. Math. Appl."},{"key":"132_CR3","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1090\/pspum\/007\/0154092","volume":"7","author":"E Bishop","year":"1962","unstructured":"Bishop, E., Phelps, R.R.: The support functionals of a convex set. Proc. Symp. Pure Math. 7, 27\u201335 (1962)","journal-title":"Proc. Symp. Pure Math."},{"key":"132_CR4","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1137\/0315004","volume":"15","author":"JM Borwein","year":"1977","unstructured":"Borwein, J.M.: Proper efficient points for maximizations with respect to cones. SIAM J. Control Optim. 15, 57\u201363 (1977)","journal-title":"SIAM J. Control Optim."},{"key":"132_CR5","doi-asserted-by":"crossref","first-page":"2356","DOI":"10.1016\/j.na.2009.10.036","volume":"72","author":"E Casinia","year":"2010","unstructured":"Casinia, E., Miglierina, E.: Cones with bounded and unbounded bases and reflexivity. Nonlinear Anal. Theory Methods Appl. 72, 2356\u20132366 (2010)","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"132_CR6","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/BF00940320","volume":"74","author":"GY Chen","year":"1992","unstructured":"Chen, G.Y.: Existence of solutions for a vector variational inequality: an extension of the Hartmann\u2013Stampacchia Theorem. J. Optim. Theory Appl. 74, 445\u2013456 (1992)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"132_CR7","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1023\/A:1013044529035","volume":"112","author":"GY Chen","year":"2002","unstructured":"Chen, G.Y., Yang, X.Q.: Characterizations of variable domination structures via nonlinear scalarization. J. Optim. Theory Appl. 112(1), 97\u2013110 (2002)","journal-title":"J. Optim. Theory Appl."},{"key":"132_CR8","volume-title":"Vector Optimization, Set-Valued and Variational Analysis","author":"G-Y Chen","year":"2005","unstructured":"Chen, G.-Y., Huang, X., Yang, X.: Vector Optimization, Set-Valued and Variational Analysis. Springer, Berlin (2005)"},{"key":"132_CR9","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1007\/s10898-003-2683-2","volume":"32","author":"GY Chen","year":"2005","unstructured":"Chen, G.Y., Yang, X.Q., Yu, H.: A nonlinear scalarization function and generalized quasi-vector equilibrium problems. J. Glob. Optim. 32, 451\u2013466 (2005)","journal-title":"J. Glob. Optim."},{"issue":"2","key":"132_CR10","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s10957-011-9928-x","volume":"151","author":"G Eichfelder","year":"2011","unstructured":"Eichfelder, G.: Optimal elements in vector optimization with a variable ordering structure. J. Optim. Theory Appl. 151(2), 217\u2013240 (2011)","journal-title":"J. Optim. Theory Appl."},{"key":"132_CR11","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/978-3-642-21114-0_4","volume-title":"Chapter 4 in: Recent Developments in Vector Optimization","author":"G Eichfelder","year":"2012","unstructured":"Eichfelder, G.: Variable ordering structures in vector optimization. In: Ansari, Q.H., Yao, J.-C. (eds.) Chapter 4 in: Recent Developments in Vector Optimization, pp. 95\u2013126. Springer, Heidelberg (2012)"},{"key":"132_CR12","doi-asserted-by":"crossref","unstructured":"Eichfelder, G.: Numerical procedures in multiobjective optimization with variable ordering structures. J. Optim. Theory Appl. (2013). doi: 10.1007\/s10957-013-0267-y","DOI":"10.1007\/s10957-013-0267-y"},{"issue":"5","key":"132_CR13","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(5), 597\u2013627 (2013)","journal-title":"Optimization"},{"key":"132_CR14","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":"132_CR15","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/978-3-642-56680-6_17","volume":"507","author":"RN Gasimov","year":"2001","unstructured":"Gasimov, R.N.: Characterization of the Benson proper efficiency and scalarization in nonconvex vector optimization. Lect. Notes Econ. Math. Syst. 507, 189\u2013198 (2001)","journal-title":"Lect. Notes Econ. Math. Syst."},{"key":"132_CR16","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.ejor.2006.03.016","volume":"179","author":"RN Gasmiov","year":"2007","unstructured":"Gasmiov, R.N., Sipahio\u01e7lu, A., Sara\u00e7, T.: A multi-objective programming approach to 1.5-dimensional assortment problem. Eur. J. Oper. Res. 179, 64\u201379 (2007)","journal-title":"Eur. J. Oper. Res."},{"key":"132_CR17","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1016\/0022-247X(68)90201-1","volume":"22","author":"AM Geoffrion","year":"1968","unstructured":"Geoffrion, A.M.: Proper efficiency and the theory of vector maximization. J. Math. Anal. Appl. 22, 618\u2013630 (1968)","journal-title":"J. Math. Anal. Appl."},{"key":"132_CR18","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/BF00940478","volume":"67","author":"C Gerth","year":"1990","unstructured":"Gerth, C., Weidner, P.: Nonconvex separation theorems and some applications in vector optimization. J. Optim. Theory Appl. 67, 297\u2013320 (1990)","journal-title":"J. Optim. Theory Appl."},{"key":"132_CR19","volume-title":"Variational Methods in Partially Ordered Spaces","author":"A G\u00f6pfert","year":"2003","unstructured":"G\u00f6pfert, A., Riahi, H., Tammer, C., Z\u0103linescu, C.: Variational Methods in Partially Ordered Spaces. Springer, New York (2003)"},{"key":"132_CR20","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/BF00934353","volume":"36","author":"I Henig","year":"1982","unstructured":"Henig, I.: Proper efficiency with respect to cones. J. Optim. Theory Appl. 36, 387\u2013407 (1982)","journal-title":"J. Optim. Theory Appl."},{"key":"132_CR21","doi-asserted-by":"crossref","unstructured":"Hirsch, C., Shukla, P.K., Schmeck, H.: Variable preference modeling using multi-objective evolutionary algorithms. In: Takahashi et al. R.H.C. (eds.) Evolutionary Multi-Criterion Optimization-6th International Conference, Lecture Notes in Computer Science 6576. Springer, Heidelberg (2011)","DOI":"10.1007\/978-3-642-19893-9_7"},{"key":"132_CR22","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1016\/j.mcm.2007.03.012","volume":"46","author":"NA Ismayilova","year":"2007","unstructured":"Ismayilova, N.A., Ozdemir, M.S., Gasimov, R.N.: A multi-objective faculty-course-time slot assignment problem with preferences. Math. Comput. Model. 46, 1017\u20131029 (2007)","journal-title":"Math. Comput. Model."},{"key":"132_CR23","first-page":"123","volume":"1","author":"J Jahn","year":"2009","unstructured":"Jahn, J.: Bishop\u2013Phelps cones in optimization. Int. J. Optim. Theory Methods Appl. 1, 123\u2013139 (2009)","journal-title":"Int. J. Optim. Theory Methods Appl."},{"key":"132_CR24","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, Heidelberg (2011)","edition":"2"},{"key":"132_CR25","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1080\/02331930902928310","volume":"58","author":"R Kasimbeyli","year":"2009","unstructured":"Kasimbeyli, R.: Radial epiderivatives and set-valued optimization. Optimization 58, 521\u2013534 (2009)","journal-title":"Optimization"},{"key":"132_CR26","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1137\/070694089","volume":"20","author":"R Kasimbeyli","year":"2010","unstructured":"Kasimbeyli, R.: A nonlinear cone separation theorem and scalarization in nonconvex vector optimization. SIAM J. Optim. 20, 1591\u20131619 (2010)","journal-title":"SIAM J. Optim."},{"issue":"2","key":"132_CR27","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s10898-011-9789-8","volume":"56","author":"R Kasimbeyli","year":"2013","unstructured":"Kasimbeyli, R.: A conic scalarization method in multi-objective optimization. J. Glob. Optim. 56(2), 279\u2013297 (2013)","journal-title":"J. Glob. Optim."},{"key":"132_CR28","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1137\/080738106","volume":"20","author":"R Kasimbeyli","year":"2009","unstructured":"Kasimbeyli, R., Mammadov, M.: On weak subdifferentials, directional derivatives and radial epiderivatives for nonconvex functions. SIAM J. Optim. 20, 841\u2013855 (2009)","journal-title":"SIAM J. Optim."},{"key":"132_CR29","doi-asserted-by":"crossref","first-page":"2534","DOI":"10.1016\/j.na.2010.12.008","volume":"74","author":"R Kasimbeyli","year":"2011","unstructured":"Kasimbeyli, R., Mammadov, M.: Optimality conditions in nonconvex optimization via weak subdifferentials. Nonlinear Anal. Theory Methods Appl. 74, 2534\u20132547 (2011)","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"132_CR30","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1007\/BF00934564","volume":"42","author":"A Pascoletti","year":"1984","unstructured":"Pascoletti, A., Serafini, P.: Scalarizing vector optimization problems. J. Optim. Theory Appl. 42, 499\u2013524 (1984)","journal-title":"J. Optim. Theory Appl."},{"key":"132_CR31","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1137\/0328021","volume":"28","author":"M Petschke","year":"1990","unstructured":"Petschke, M.: On a theorem of Arrow, Barankin, and Blackwell. SIAM J. Control Optim. 28, 395\u2013401 (1990)","journal-title":"SIAM J. Control Optim."},{"key":"132_CR32","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.jmaa.2003.08.033","volume":"289","author":"IA Polyrakis","year":"2004","unstructured":"Polyrakis, I.A.: Embeddability of $$L_1(\\mu )$$ L 1 ( \u03bc ) in dual spaces, geometry of cones and a characterization of $$c_0$$ c 0 . J. Math. Anal. Appl. 289, 126\u2013142 (2004)","journal-title":"J. Math. Anal. Appl."},{"key":"132_CR33","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1023\/B:JOGO.0000047914.22567.66","volume":"29","author":"AM Rubinov","year":"2004","unstructured":"Rubinov, A.M., Gasimov, R.N.: Scalarization and nonlinear scalar duality for vector optimization with preferences that are not necessarily a pre-order relation. J. Glob. Optim. 29, 455\u2013477 (2004)","journal-title":"J. Glob. Optim."},{"key":"132_CR34","unstructured":"Wacker, M.: Multikriterielle Optimierung bei der Registrierung medizinischer Daten. Diploma thesis, Univ. Erlangen-N\u00fcrnberg (2008)"},{"key":"132_CR35","doi-asserted-by":"crossref","unstructured":"Wacker M., Deinzer, F.: Automatic robust medical image registration using a new democratic vector optimization approach with multiple measures. In: Yang et al. G.-Z. (eds) Medical Image Computing and Computer-Assisted Intervention MICCAI 2009, pp. 590\u2013597 (2009)","DOI":"10.1007\/978-3-642-04268-3_73"},{"key":"132_CR36","first-page":"153","volume":"1","author":"MM Wiecek","year":"2007","unstructured":"Wiecek, M.M.: Advances in cone-based preference modeling for decision making with multiple criteria. Decis. Mak. Manuf. Serv. 1, 153\u2013173 (2007)","journal-title":"Decis. Mak. Manuf. Serv."},{"key":"132_CR37","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/BF00932614","volume":"14","author":"PL Yu","year":"1974","unstructured":"Yu, P.L.: Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives. J. Optim. Theory Appl. 14, 319\u2013377 (1974)","journal-title":"J. Optim. Theory Appl."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-013-0132-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10898-013-0132-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-013-0132-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,9]],"date-time":"2023-07-09T09:15:09Z","timestamp":1688894109000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10898-013-0132-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,28]]},"references-count":37,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["132"],"URL":"https:\/\/doi.org\/10.1007\/s10898-013-0132-4","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12,28]]}}}