{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,15]],"date-time":"2026-02-15T08:46:28Z","timestamp":1771145188137,"version":"3.50.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2014,4,2]],"date-time":"2014-04-02T00:00:00Z","timestamp":1396396800000},"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":[[2015,2]]},"DOI":"10.1007\/s10957-014-0558-y","type":"journal-article","created":{"date-parts":[[2014,4,1]],"date-time":"2014-04-01T15:02:28Z","timestamp":1396364548000},"page":"455-478","source":"Crossref","is-referenced-by-count":24,"title":["Characterizing Efficiency on Infinite-dimensional Commodity Spaces with Ordering Cones Having Possibly Empty Interior"],"prefix":"10.1007","volume":"164","author":[{"given":"Fabi\u00e1n","family":"Flores-Baz\u00e1n","sequence":"first","affiliation":[]},{"given":"Fernando","family":"Flores-Baz\u00e1n","sequence":"additional","affiliation":[]},{"given":"Sigifredo","family":"Laengle","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,4,2]]},"reference":[{"key":"558_CR1","doi-asserted-by":"crossref","first-page":"1075","DOI":"10.2307\/1911262","volume":"55","author":"William R Zame","year":"1987","unstructured":"Zame, William R.: Competitive equilibria in production economies with an infinite-dimensional commodity space. Econometrica 55, 1075\u20131108 (1987)","journal-title":"Econometrica"},{"key":"558_CR2","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/s00199-006-0096-4","volume":"31","author":"J-M Bonnisseau","year":"2007","unstructured":"Bonnisseau, J.-M., Crettez, B.: On the characterization of efficient production vectors. Econ. Theor. 31, 213\u2013223 (2007)","journal-title":"Econ. Theor."},{"key":"558_CR3","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/0304-4068(88)90003-1","volume":"17","author":"J-M Bonnisseau","year":"1988","unstructured":"Bonnisseau, J.-M., Cornet, B.: Existence of equilibria when firms follows bounded losses pricing rules. J. Math. Econ. 17, 119\u2013147 (1988)","journal-title":"J. Math. Econ."},{"key":"558_CR4","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. 2. Springer, Berlin (1989)"},{"key":"558_CR5","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)"},{"issue":"1","key":"558_CR6","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/s10898-007-9165-x","volume":"41","author":"F Flores-Baz\u00e1n","year":"2008","unstructured":"Flores-Baz\u00e1n, F., Hern\u00e1ndez, E., Novo, V.: Characterizing efficiency without linear structure: a unified approach. J. Global Optim. 41(1), 43\u201360 (2008)","journal-title":"J. Global Optim."},{"key":"558_CR7","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1080\/02331934.2011.641018","volume":"60","author":"F Flores-Baz\u00e1n","year":"2011","unstructured":"Flores-Baz\u00e1n, F., Hern\u00e1ndez, E.: A unified vector optimization problem: complete scalarizations and applications. Optimization 60, 1399\u20131419 (2011)","journal-title":"Optimization"},{"key":"558_CR8","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":"558_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-79159-1","volume-title":"Adaptive Scalarization Methods in Multiobjective Optimization","author":"G Eichfelder","year":"2008","unstructured":"Eichfelder, G.: Adaptive Scalarization Methods in Multiobjective Optimization. Springer, Berlin (2008)"},{"key":"558_CR10","doi-asserted-by":"crossref","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 via a general scalarization. Optimization 60, 1269\u20131290 (2011)","journal-title":"Optimization"},{"key":"558_CR11","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":"558_CR12","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":"558_CR13","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1007\/s10957-009-9609-1","volume":"145","author":"M Durea","year":"2010","unstructured":"Durea, M., Dutta, J., Tammer, C.: Lagrange multipliers for $$\\varepsilon $$ \u03b5 -Pareto solutions in vector optimization with nonsolid cones in Banach spaces. J. Optim. Theory Appl. 145, 196\u2013211 (2010)","journal-title":"J. Optim. Theory Appl."},{"key":"558_CR14","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/BF00941466","volume":"75","author":"DG Luenberger","year":"1992","unstructured":"Luenberger, D.G.: New optimality principles for economics efficiency and equilibrium. J. Optim. Theory Appl. 75, 221\u2013264 (1992)","journal-title":"J. Optim. Theory Appl."},{"key":"558_CR15","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":"558_CR16","first-page":"61","volume":"31","author":"CH Gerstewitz","year":"1985","unstructured":"Gerstewitz, C.H., Iwanow, E.: Dualit $$\\ddot{\\text{ a }}$$ a \u00a8 t f $$\\ddot{\\text{ u }}$$ u \u00a8 r nichtkonvexe Vektoroptimierungsprobleme. Wiss. Z. Tech. Hochsch. Ilmenau 31, 61\u201381 (1985)","journal-title":"Wiss. Z. Tech. Hochsch. Ilmenau"},{"key":"558_CR17","first-page":"113","volume":"32","author":"AM Rubinov","year":"1977","unstructured":"Rubinov, A.M.: Sublinear operator and theirs applications. Rus. Math. Surveys 32, 113\u2013175 (1977)","journal-title":"Rus. Math. Surveys"},{"key":"558_CR18","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 preorder relation. J. Global Optim. 29, 455\u2013477 (2004)","journal-title":"J. Global Optim."},{"key":"558_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":"558_CR20","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1080\/02331930801951033","volume":"59","author":"C Tammer","year":"2010","unstructured":"Tammer, C., Zalinescu, C.: Lipschitz properties of the scalarization function and applications. Optimization 59, 305\u2013319 (2010)","journal-title":"Optimization"},{"key":"558_CR21","volume-title":"Variational Methods in Partially Ordered Spaces. CMS Books in Mathematics","author":"A G\u00f6pfert","year":"2003","unstructured":"G\u00f6pfert, A., Riahi, H., Tammer, Ch., Zalinescu, C.: Variational Methods in Partially Ordered Spaces. CMS Books in Mathematics. Springer, New york (2003)"},{"key":"558_CR22","unstructured":"Chen, G-Y.; Huang, X.; Yang, X., \u201cVector optimization. Set-valued and variational analysis\u201d. Lecture Notes in Economics and Mathematical Systems, 541. Springer-Verlag, Berlin, 2005."},{"key":"558_CR23","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1137\/05062648X","volume":"17","author":"C Guti\u00e9rrez","year":"2006","unstructured":"Guti\u00e9rrez, C., Jim\u00e9nez, B., Novo, V.: A unified approach and optimality conditions for approximate solutions of vector optimization problems. SIAM J. Optim. 17, 688\u2013710 (2006)","journal-title":"SIAM J. Optim."},{"key":"558_CR24","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":"558_CR25","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/j.ejor.2012.05.050","volume":"223","author":"C Guti\u00e9rrez","year":"2012","unstructured":"Guti\u00e9rrez, C., Jim\u00e9nez, B., Novo, V.: Improvements sets and vector optimization. Eur. J. Oper. Res. 223, 304\u2013311 (2012)","journal-title":"Eur. J. Oper. Res."},{"key":"558_CR26","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1080\/02331938808843317","volume":"19","author":"P Weidner","year":"1988","unstructured":"Weidner, P.: On the characterization of efficient points by means of monotone functionals. Optimization 19, 53\u201369 (1988)","journal-title":"Optimization"},{"key":"558_CR27","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/BF01581072","volume":"57","author":"JM Borwein","year":"1992","unstructured":"Borwein, J.M., Lewis, A.S.: Partially finite convex programming, Part I: quasi relative interiors and duality theory. Math. Program. A 57, 15\u201348 (1992)","journal-title":"Math. Program. A"},{"key":"558_CR28","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/BF00940705","volume":"78","author":"MA Limber","year":"1993","unstructured":"Limber, M.A., Goodrich, R.K.: Quasi interiors, Lagrange multipliers, and $$L^p$$ L p spectral estimation with lattice bounds. J. Optim. Theory Appl. 78, 143\u2013161 (1993)","journal-title":"J. Optim. Theory Appl."},{"key":"558_CR29","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.jmaa.2009.09.006","volume":"361","author":"A Grad","year":"2010","unstructured":"Grad, A.: Quasi-relative interior-type constraint qualifications ensuring strong Lagrange duality for optimization problems with cone and affine constraints. J. Math. Anal. Appl. 361, 86\u201395 (2010)","journal-title":"J. Math. Anal. Appl."},{"key":"558_CR30","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/S0022-247X(02)00410-9","volume":"283","author":"SJ Li","year":"2003","unstructured":"Li, S.J., Yang, X.Q., Chen, G.Y.: Nonconvex vector optimization of set-valued mappings. J. Math. Anal. Appl. 283, 337\u2013350 (2003)","journal-title":"J. Math. Anal. Appl."},{"key":"558_CR31","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1007\/s007800200072","volume":"6","author":"H Follmer","year":"2002","unstructured":"Follmer, H., Schied, A.: Convex measures of risk and trading constraints. Financ. Stoch. 6, 429\u2013447 (2002)","journal-title":"Financ. Stoch."},{"key":"558_CR32","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1006\/jmaa.1993.1368","volume":"179","author":"V Jeyakumar","year":"1993","unstructured":"Jeyakumar, V., Oettli, W., Natividad, M.: A solvability theorem for a class of quasiconvex mappings with applications to optimization. J. Math. Anal. Appl. 179, 537\u2013546 (1993)","journal-title":"J. Math. Anal. Appl."},{"key":"558_CR33","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s10107-006-0071-7","volume":"111","author":"LDG Drummond","year":"2008","unstructured":"Drummond, L.D.G., Maculan, N., Svaiter, B.F.: On the choice of parameter for the weighting method in vector optimization. Math. Program. Ser. B 111, 201\u2013216 (2008)","journal-title":"Math. Program. Ser. B"},{"key":"558_CR34","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1007\/s10957-011-9851-1","volume":"150","author":"M Chicco","year":"2011","unstructured":"Chicco, M., Mignanego, F., Pusillo, L., Tijs, S.: Vector optimization problems via improvements sets. J. Optim. Theory Appl. 150, 516\u2013529 (2011)","journal-title":"J. Optim. Theory Appl."},{"key":"558_CR35","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s10898-011-9822-y","volume":"56","author":"F Flores-Baz\u00e1n","year":"2013","unstructured":"Flores-Baz\u00e1n, F., Hern\u00e1ndez, E.: Optimality conditions for a unified vector optimization problem with not necessarily preordering relations. J. Global Optim. 56, 299\u2013325 (2013)","journal-title":"J. Global Optim."},{"key":"558_CR36","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":"558_CR37","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. Program. A 122, 301\u2013347 (2010)","journal-title":"Math. Program. A"},{"key":"558_CR38","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-21893-8","volume-title":"Existence and optimality of competitive equilibria","author":"CD Aliprantis","year":"1989","unstructured":"Aliprantis, C.D., Brown, D.J., Burkinshaw, O.: Existence and optimality of competitive equilibria. Springer, Berlin (1989)"},{"key":"558_CR39","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s10100-011-0233-4","volume":"21","author":"F Flores-Baz\u00e1n","year":"2013","unstructured":"Flores-Baz\u00e1n, F., Laengle, S., Loyola, G.: Characterizing the efficient points without closedness or free-disposability. Cent. Eur. J. Oper. Res. 21, 401\u2013410 (2013)","journal-title":"Cent. Eur. J. Oper. Res."},{"key":"558_CR40","volume-title":"Theory of Value","author":"G Debreu","year":"1959","unstructured":"Debreu, G.: Theory of Value. Wiley, New York (1959)"},{"key":"558_CR41","volume-title":"Theory of incomplete markets","author":"M Magill","year":"1996","unstructured":"Magill, M., Quinzii, M.: Theory of incomplete markets, vol. 1. MIT Press, Cambridge (1996)"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-014-0558-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-014-0558-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-014-0558-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T05:58:37Z","timestamp":1559455117000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-014-0558-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4,2]]},"references-count":41,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,2]]}},"alternative-id":["558"],"URL":"https:\/\/doi.org\/10.1007\/s10957-014-0558-y","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,4,2]]}}}