{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T22:34:30Z","timestamp":1769726070601,"version":"3.49.0"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,9,30]],"date-time":"2024-09-30T00:00:00Z","timestamp":1727654400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,9,30]],"date-time":"2024-09-30T00:00:00Z","timestamp":1727654400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100006115","name":"Institute for Research in Fundamental Sciences","doi-asserted-by":"publisher","award":["1402490038"],"award-info":[{"award-number":["1402490038"]}],"id":[{"id":"10.13039\/501100006115","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006115","name":"Institute for Research in Fundamental Sciences","doi-asserted-by":"publisher","award":["1403460315"],"award-info":[{"award-number":["1403460315"]}],"id":[{"id":"10.13039\/501100006115","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Glob Optim"],"published-print":{"date-parts":[[2025,1]]},"DOI":"10.1007\/s10898-024-01431-y","type":"journal-article","created":{"date-parts":[[2024,9,30]],"date-time":"2024-09-30T02:01:45Z","timestamp":1727661705000},"page":"199-215","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Existence of weak efficient solutions of set-valued optimization problems"],"prefix":"10.1007","volume":"91","author":[{"given":"Fatemeh","family":"Fakhar","sequence":"first","affiliation":[]},{"given":"Hamid Reza","family":"Hajisharifi","sequence":"additional","affiliation":[]},{"given":"Zeinab","family":"Soltani","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,9,30]]},"reference":[{"issue":"4","key":"1431_CR1","doi-asserted-by":"publisher","first-page":"2847","DOI":"10.1137\/15M1054997","volume":"26","author":"A Amini-Harandi","year":"2016","unstructured":"Amini-Harandi, A., Fakhar, M., Hajisharifi, H.R.: Some generalizations of the Weierstrass theorem. SIAM J. Optim. 26(4), 2847\u20132862 (2016)","journal-title":"SIAM J. Optim."},{"issue":"4","key":"1431_CR2","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1287\/moor.21.4.769","volume":"21","author":"A Auslender","year":"1996","unstructured":"Auslender, A.: Noncoercive optimization problems. Math. Oper. Res. 21(4), 769\u2013782 (1996)","journal-title":"Math. Oper. Res."},{"issue":"2","key":"1431_CR3","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/BF00282202","volume":"100","author":"C Baiocchi","year":"1988","unstructured":"Baiocchi, C., Buttazzo, G., Gastaldi, F., Tomarelli, F.: General existence theorems for unilateral problems in continuum mechanics. Arch. J. Ration. Mech. Anal. 100(2), 149\u2013189 (1988)","journal-title":"Arch. J. Ration. Mech. Anal."},{"key":"1431_CR4","volume-title":"Vector Optimization: Set-Valued and Variational Analysis. LNEMS","author":"GY Chen","year":"2006","unstructured":"Chen, G.Y., Huang, X.X., Yang, X.: Vector Optimization: Set-Valued and Variational Analysis. LNEMS, vol. 541. Springer, Berlin (2006)"},{"issue":"5","key":"1431_CR5","doi-asserted-by":"publisher","first-page":"1589","DOI":"10.1080\/02331934.2023.2170699","volume":"73","author":"M Chinaie","year":"2023","unstructured":"Chinaie, M., Fakhar, F., Fakhar, M., Hajisharifi, H.R.: Strict weak $$l$$-efficient solutions for nonconvex set optimization problems. Optimization 73(5), 1589\u20131609 (2023)","journal-title":"Optimization"},{"key":"1431_CR6","volume-title":"Recent Developments in Vector Optimization","author":"G Eichfelder","year":"2011","unstructured":"Eichfelder, G.: Variable ordering structures in vector optimization. In: Ansari, Q.H., Yao, J.C. (eds.) Recent Developments in Vector Optimization. Springer, Heidelberg (2011)"},{"issue":"4","key":"1431_CR7","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1007\/s10898-023-01289-6","volume":"86","author":"F Fakhar","year":"2023","unstructured":"Fakhar, F., Hajisharifi, H.R., Soltani, Z.: Noncoercive and noncontinuous equilibrium problems: existence theorem in infinite-dimensional spaces. J. Glob. Optim. 86(4), 989\u20131003 (2023)","journal-title":"J. Glob. Optim."},{"key":"1431_CR8","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1007\/s10107-002-0311-4","volume":"93","author":"F Flores-Baz\u00e1n","year":"2002","unstructured":"Flores-Baz\u00e1n, F.: Ideal, weakly efficient solutions for vector optimization problems. Math. Program. 93, 453\u2013475 (2002)","journal-title":"Math. Program."},{"key":"1431_CR9","doi-asserted-by":"publisher","first-page":"880","DOI":"10.1007\/s10957-020-01667-0","volume":"185","author":"C Guti\u00e9rrez","year":"2020","unstructured":"Guti\u00e9rrez, C., L\u00f3pez, R.: On the existence of weak efficient solutions of nonconvex vector optimization problems. J. Optim. Theory Appl. 185, 880\u2013902 (2020)","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"1431_CR10","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":"4","key":"1431_CR11","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."},{"issue":"1","key":"1431_CR12","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1007\/s10957-018-1317-2","volume":"180","author":"N Hadjisavvas","year":"2019","unstructured":"Hadjisavvas, N., Lara, F., Mart\u00ednez-Legaz, J.E.: A quasi-convex asymptotic function with applications in optimization. J. Optim. Theory Appl. 180(1), 170\u2013186 (2019)","journal-title":"J. Optim. Theory Appl."},{"key":"1431_CR13","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1007\/s11228-018-0468-5","volume":"27","author":"E Hern\u00e1ndez","year":"2019","unstructured":"Hern\u00e1ndez, E., L\u00f3pez, R.: About asymptotic analysis and set optimization. Set-Valued Var. Anal. 27, 643\u2013664 (2019)","journal-title":"Set-Valued Var. Anal."},{"key":"1431_CR14","doi-asserted-by":"publisher","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."},{"issue":"2","key":"1431_CR15","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1016\/S0362-546X(02)00154-2","volume":"52","author":"A Iusem","year":"2003","unstructured":"Iusem, A., Sosa, W.: New existence results for equilibrium problems. Nonlinear Anal. 52(2), 621\u2013635 (2003)","journal-title":"Nonlinear Anal."},{"key":"1431_CR16","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)"},{"key":"1431_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-54265-7","volume-title":"Set-Valued Optimization: An Introduction with Applications. Vector Optimization","author":"AA Khan","year":"2015","unstructured":"Khan, A.A., Tammer, Ch., Z\u0103linescu, C.: Set-Valued Optimization: An Introduction with Applications. Vector Optimization. Springer, Heidelberg (2015)"},{"key":"1431_CR18","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1007\/s11590-016-1027-3","volume":"11","author":"S Khoshkhabar-amiranloo","year":"2017","unstructured":"Khoshkhabar-amiranloo, S., Khorram, E., Soleimani-damaneh, M.: Nonlinear scalarization functions and polar cone in set optimization. Optim. Lett. 11, 521\u2013535 (2017)","journal-title":"Optim. Lett."},{"key":"1431_CR19","first-page":"85","volume":"1031","author":"D Kuroiwa","year":"1998","unstructured":"Kuroiwa, D.: The natural criteria in set-valued optimization. Research on nonlinear analysis and convex analysis (Japanese) (Kyoto, 1997). Surikaisekikenkyusho Kokyuroku 1031, 85\u201390 (1998)","journal-title":"Surikaisekikenkyusho Kokyuroku"},{"issue":"2","key":"1431_CR20","doi-asserted-by":"publisher","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(2), 1395\u20131400 (2001)","journal-title":"Nonlinear Anal."},{"issue":"1","key":"1431_CR21","first-page":"73","volume":"24","author":"D Kuroiwa","year":"2003","unstructured":"Kuroiwa, D.: Existence theorems of set optimization with set-valued maps. J. Inf. Optim. Sci. 24(1), 73\u201384 (2003)","journal-title":"J. Inf. Optim. Sci."},{"key":"1431_CR22","doi-asserted-by":"publisher","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)"},{"issue":"2","key":"1431_CR23","doi-asserted-by":"publisher","first-page":"544","DOI":"10.1016\/j.jmaa.2009.10.040","volume":"364","author":"DT Luc","year":"2010","unstructured":"Luc, D.T., Sarabi, E., Soubeyran, A.: Existence of solutions in variational relation problems without convexity. J. Math. Anal. Appl. 364(2), 544\u2013555 (2010)","journal-title":"J. Math. Anal. Appl."},{"key":"1431_CR24","first-page":"249","volume":"19","author":"M Marinacci","year":"2012","unstructured":"Marinacci, M., Montrucchio, L.: Finitely well-positioned sets. J. Convex Anal. 19, 249\u2013279 (2012)","journal-title":"J. Convex Anal."},{"issue":"3\u20134","key":"1431_CR25","first-page":"205","volume":"49","author":"JP Penot","year":"2006","unstructured":"Penot, J.P.: Noncoercive problems and asymptotic conditions. Asymptot. Anal. 49(3\u20134), 205\u2013215 (2006)","journal-title":"Asymptot. Anal."}],"container-title":["Journal of Global Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-024-01431-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10898-024-01431-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10898-024-01431-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,11]],"date-time":"2025-01-11T09:03:25Z","timestamp":1736586205000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10898-024-01431-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,30]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["1431"],"URL":"https:\/\/doi.org\/10.1007\/s10898-024-01431-y","relation":{},"ISSN":["0925-5001","1573-2916"],"issn-type":[{"value":"0925-5001","type":"print"},{"value":"1573-2916","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,30]]},"assertion":[{"value":"14 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 September 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 September 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"We approve.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to participate"}},{"value":"We have consent for publication.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}]}}