{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T14:04:07Z","timestamp":1781013847301,"version":"3.54.1"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,5,16]],"date-time":"2020-05-16T00:00:00Z","timestamp":1589587200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,5,16]],"date-time":"2020-05-16T00:00:00Z","timestamp":1589587200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2020,6]]},"DOI":"10.1007\/s10957-020-01667-0","type":"journal-article","created":{"date-parts":[[2020,5,16]],"date-time":"2020-05-16T03:44:11Z","timestamp":1589600651000},"page":"880-902","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["On the Existence of Weak Efficient Solutions of Nonconvex Vector Optimization Problems"],"prefix":"10.1007","volume":"185","author":[{"given":"C\u00e9sar","family":"Guti\u00e9rrez","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rub\u00e9n","family":"L\u00f3pez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2020,5,16]]},"reference":[{"key":"1667_CR1","first-page":"305","volume-title":"Nonlinear Analysis and Variational Problems. Springer Optimization and Its Applications","author":"TXD Ha","year":"2010","unstructured":"Ha, T.X.D.: Optimality conditions for several types of efficient solutions of set-valued optimization problems. In: Pardalos, P., Rassias, T., Khan, A. (eds.) Nonlinear Analysis and Variational Problems. Springer Optimization and Its Applications, vol. 35, pp. 305\u2013324. Springer, New York (2010)"},{"issue":"3","key":"1667_CR2","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1080\/02331930500096213","volume":"54","author":"N Popovici","year":"2005","unstructured":"Popovici, N.: Pareto reducible multicriteria optimization problems. Optimization 54(3), 253\u2013263 (2005)","journal-title":"Optimization"},{"issue":"1","key":"1667_CR3","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1023\/A:1022615217553","volume":"96","author":"S Deng","year":"1998","unstructured":"Deng, S.: Characterizations of the nonemptiness and compactness of solution sets in convex vector optimization. J. Optim. Theory Appl. 96(1), 123\u2013131 (1998)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"1667_CR4","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1023\/A:1022627520279","volume":"96","author":"S Deng","year":"1998","unstructured":"Deng, S.: On efficient solutions in vector optimization. J. Optim. Theory Appl. 96(1), 201\u2013209 (1998)","journal-title":"J. Optim. Theory Appl."},{"issue":"1","key":"1667_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10957-008-9443-x","volume":"140","author":"S Deng","year":"2009","unstructured":"Deng, S.: Characterizations of the nonemptiness and boundedness of weakly efficient solution sets of convex vector optimization problems in real reflexive Banach spaces. J. Optim. Theory Appl. 140(1), 1\u20137 (2009)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"1667_CR6","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1006\/jmaa.2001.7635","volume":"264","author":"XX Huang","year":"2001","unstructured":"Huang, X.X., Yang, X.Q.: Characterizations of nonemptiness and compactness of the set of weakly efficient solutions for convex vector optimization and applications. J. Math. Anal. Appl. 264(2), 270\u2013287 (2001)","journal-title":"J. Math. Anal. Appl."},{"issue":"2","key":"1667_CR7","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/s10957-004-5155-z","volume":"123","author":"XX Huang","year":"2004","unstructured":"Huang, X.X., Yang, X.Q., Teo, K.L.: Characterizing nonemptiness and compactness of the solution set of a convex vector optimization problem with cone constraints and applications. J. Optim. Theory Appl. 123(2), 391\u2013407 (2004)","journal-title":"J. Optim. Theory Appl."},{"issue":"5","key":"1667_CR8","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1016\/j.orl.2008.03.002","volume":"36","author":"R L\u00f3pez","year":"2008","unstructured":"L\u00f3pez, R., Vera, C.: On the set of weakly efficient minimizers for convex multiobjective programming. Oper. Res. Lett. 36(5), 651\u2013655 (2008)","journal-title":"Oper. Res. Lett."},{"key":"1667_CR9","doi-asserted-by":"crossref","unstructured":"Flores-Baz\u00e1n, F.: Ideal, weakly efficient solutions for vector optimization problems. Math. Program. 93(3), Ser. A, 453\u2013475 (2002)","DOI":"10.1007\/s10107-002-0311-4"},{"issue":"2","key":"1667_CR10","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/s10957-006-9098-4","volume":"130","author":"F Flores-Baz\u00e1n","year":"2006","unstructured":"Flores-Baz\u00e1n, F., Vera, C.: Characterization of the nonemptiness and compactness of solution sets in convex and nonconvex vector optimization. J. Optim. Theory Appl. 130(2), 185\u2013207 (2006)","journal-title":"J. Optim. Theory Appl."},{"issue":"5","key":"1667_CR11","first-page":"895","volume":"29","author":"H Huang","year":"2005","unstructured":"Huang, H.: Characterizations for the nonemptiness and compactness of the set of weakly efficient solutions. Southeast Asian Bull. Math. 29(5), 895\u2013902 (2005)","journal-title":"Southeast Asian Bull. Math."},{"issue":"7","key":"1667_CR12","doi-asserted-by":"publisher","first-page":"1233","DOI":"10.1007\/s11590-011-0366-3","volume":"6","author":"F Flores-Baz\u00e1n","year":"2012","unstructured":"Flores-Baz\u00e1n, F., Lara, F.: Inner and outer estimates for the solution sets and their asymptotic cones in vector optimization. Optim. Lett. 6(7), 1233\u20131249 (2012)","journal-title":"Optim. Lett."},{"issue":"2","key":"1667_CR13","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1007\/s10957-014-0541-7","volume":"162","author":"C Guti\u00e9rrez","year":"2014","unstructured":"Guti\u00e9rrez, C., L\u00f3pez, R., Novo, V.: Existence and boundedness of solutions in infinite-dimensional vector optimization problems. J. Optim. Theory Appl. 162(2), 515\u2013547 (2014)","journal-title":"J. Optim. Theory Appl."},{"issue":"3","key":"1667_CR14","doi-asserted-by":"publisher","first-page":"697","DOI":"10.1007\/s10957-014-0552-4","volume":"163","author":"K Ito","year":"2014","unstructured":"Ito, K., Kunisch, K.: A note on the existence of nonsmooth nonconvex optimization problems. J. Optim. Theory Appl. 163(3), 697\u2013706 (2014)","journal-title":"J. Optim. Theory Appl."},{"key":"1667_CR15","volume-title":"Vector Optimization: Set-Valued and Variational Analysis","author":"GY Chen","year":"2005","unstructured":"Chen, G.Y., Huang, X., Yang, X.: Vector Optimization: Set-Valued and Variational Analysis. Springer, Berlin (2005)"},{"key":"1667_CR16","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)"},{"issue":"2","key":"1667_CR17","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1023\/A:1004695229456","volume":"106","author":"S Bolintin\u00e9anu","year":"2000","unstructured":"Bolintin\u00e9anu, S.: Approximate efficiency and scalar stationarity in unbounded nonsmooth convex vector optimization problems. J. Optim. Theory Appl. 106(2), 265\u2013296 (2000)","journal-title":"J. Optim. Theory Appl."},{"issue":"4","key":"1667_CR18","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1007\/s11590-011-0301-7","volume":"6","author":"M El Maghri","year":"2012","unstructured":"El Maghri, M.: Pareto\u2013Fenchel $$\\epsilon $$-subdifferential sum rule and $$\\epsilon $$-efficiency. Optim. Lett. 6(4), 763\u2013781 (2012)","journal-title":"Optim. Lett."},{"issue":"1","key":"1667_CR19","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/0022-247X(92)90237-8","volume":"167","author":"T Tanino","year":"1992","unstructured":"Tanino, T.: Conjugate duality in vector optimization. J. Math. Anal. Appl. 167(1), 84\u201397 (1992)","journal-title":"J. Math. Anal. Appl."},{"issue":"2","key":"1667_CR20","first-page":"119","volume":"18","author":"C Combari","year":"1994","unstructured":"Combari, C., Laghdir, M., Thibault, L.: Sous-diff\u00e9rentiels de fonctions convexes compos\u00e9es. Ann. Sci. Math. Qu\u00e9bec 18(2), 119\u2013148 (1994)","journal-title":"Ann. Sci. Math. Qu\u00e9bec"},{"key":"1667_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-50280-4","volume-title":"Theory of Vector Optimization","author":"D Luc","year":"1989","unstructured":"Luc, D.: Theory of Vector Optimization. Springer, Berlin (1989)"},{"issue":"3","key":"1667_CR22","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1007\/s10957-019-01486-y","volume":"181","author":"F Flores-Baz\u00e1n","year":"2019","unstructured":"Flores-Baz\u00e1n, F., Mastroeni, G., Vera, C.: Proper or weak efficiency via saddle point conditions in cone-constrained nonconvex vector optimization problems. J. Optim. Theory Appl. 181(3), 787\u2013816 (2019)","journal-title":"J. Optim. Theory Appl."},{"key":"1667_CR23","volume-title":"Noncoercive Variational Problems and Related Results","author":"D Goeleven","year":"1996","unstructured":"Goeleven, D.: Noncoercive Variational Problems and Related Results. Longman, Harlow (1996)"},{"key":"1667_CR24","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718782","volume-title":"Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization","author":"H Attouch","year":"2006","unstructured":"Attouch, H., Buttazzo, G., Michaille, G.: Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization. SIAM, Philadelphia (2006)"},{"issue":"2\u20133","key":"1667_CR25","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1080\/02331939208843815","volume":"25","author":"C Tammer","year":"1992","unstructured":"Tammer, C.: A generalization of Ekeland\u2019s variational principle. Optimization 25(2\u20133), 129\u2013141 (1992)","journal-title":"Optimization"},{"issue":"2","key":"1667_CR26","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1007\/BF01304771","volume":"38","author":"JP Penot","year":"1982","unstructured":"Penot, J.P., Th\u00e9ra, M.: Semicontinuous mappings in general topology. Arch. Math. (Basel) 38(2), 158\u2013166 (1982)","journal-title":"Arch. Math. (Basel)"},{"issue":"1\u20132","key":"1667_CR27","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1080\/02331930600808178","volume":"56","author":"MA Mansour","year":"2007","unstructured":"Mansour, M.A., Malivert, C., Th\u00e9ra, M.: Semicontinuity of vector-valued mappings. Optimization 56(1\u20132), 241\u2013252 (2007)","journal-title":"Optimization"},{"issue":"3","key":"1667_CR28","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1023\/A:1022603406244","volume":"92","author":"M Bianchi","year":"1997","unstructured":"Bianchi, M., Hadjisavvas, N., Schaible, S.: Vector equilibrium problems with generalized monotone bifunctions. J. Optim. Theory Appl. 92(3), 527\u2013542 (1997)","journal-title":"J. Optim. Theory Appl."},{"issue":"4","key":"1667_CR29","doi-asserted-by":"publisher","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(4), 1822\u20131833 (2012)","journal-title":"Nonlinear Anal."},{"key":"1667_CR30","volume-title":"Infinite Dimensional Analysis","author":"CD Aliprantis","year":"2006","unstructured":"Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis. Springer, Berlin (2006)"},{"key":"1667_CR31","unstructured":"Bouchitt\u00e9, G., Suquet, P.: Equi-coercivity of variational problems: the role of recession functions. In: Nonlinear Partial Differential Equations and Their Applications. Pitman Research Notes in Mathematics Series, vol. 302, pp. 31\u201354. Longman Scientific & Technical, Harlow (1994)"},{"issue":"3","key":"1667_CR32","first-page":"565","volume":"20","author":"AA Khan","year":"2019","unstructured":"Khan, A.A., Hebestreit, N., K\u00f6bis, E., Tammer, C.: Existence theorems and regularization methods for non-coercive vector variational and vector quasi-variational inequalities. J. Nonlinear Convex Anal. 20(3), 565\u2013591 (2019)","journal-title":"J. Nonlinear Convex Anal."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-020-01667-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-020-01667-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-020-01667-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,15]],"date-time":"2021-05-15T23:31:58Z","timestamp":1621121518000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-020-01667-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,16]]},"references-count":32,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["1667"],"URL":"https:\/\/doi.org\/10.1007\/s10957-020-01667-0","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,16]]},"assertion":[{"value":"30 October 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 May 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}