{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,7,4]],"date-time":"2022-07-04T12:30:22Z","timestamp":1656937822189},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2016,9,12]],"date-time":"2016-09-12T00:00:00Z","timestamp":1473638400000},"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":["Optim Lett"],"published-print":{"date-parts":[[2017,12]]},"DOI":"10.1007\/s11590-016-1079-4","type":"journal-article","created":{"date-parts":[[2016,9,12]],"date-time":"2016-09-12T12:33:41Z","timestamp":1473683621000},"page":"1677-1690","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Convergence of relaxed minimizers in set optimization"],"prefix":"10.1007","volume":"11","author":[{"given":"Michel H.","family":"Geoffroy","sequence":"first","affiliation":[]},{"given":"Yvesner","family":"Marcelin","sequence":"additional","affiliation":[]},{"given":"Diana","family":"Nedelcheva","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,9,12]]},"reference":[{"key":"1079_CR1","unstructured":"Bao, T.Q., Mordukhovich, B.S.: Relative Pareto minimizers for multiobjective problems: existence and optimality conditions. Math. Program. Ser. A 122(2), 301\u2013347 (2010)"},{"key":"1079_CR2","unstructured":"Borwein, J., Goebel, R.: Notions of relative interior in Banach spaces, optimization and related topics, 1. J. Math. Sci. (N. Y.) 115(4), 2542\u20132553 (2003)"},{"key":"1079_CR3","doi-asserted-by":"crossref","unstructured":"Borwein, J., Lewis, A.S.: Partially finite convex programming. I. Quasi relative interiors and duality theory. Math. Program. Ser. B 57(1), 15\u201348 (1992) II. Explicit lattice models. Math. Program. Ser. B 57(1) 49\u201383 (1992)","DOI":"10.1007\/BF01581072"},{"key":"1079_CR4","doi-asserted-by":"crossref","unstructured":"Braides, A.: A handbook of $$\\Gamma $$ \u0393 -convergence. In: Chipot, M., Quittner, P. (Eds.) Handbook of Differential Equations. Stationary Partial Differential Equations, vol. 3, pp. 101\u2013213. Elsevier, Amsterdam (2006)","DOI":"10.1016\/S1874-5733(06)80006-9"},{"issue":"3","key":"1079_CR5","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 improvement sets. J. Optim. Theory Appl. 150(3), 516\u2013529 (2011)","journal-title":"J. Optim. Theory Appl."},{"key":"1079_CR6","unstructured":"De Giorgi, E., Franzoni, T.: Su un tipo di convergenza variazionale. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 58(6), 842\u2013850 (1975)"},{"key":"1079_CR7","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1090\/S0002-9947-1964-0175081-6","volume":"112","author":"RM Dudley","year":"1964","unstructured":"Dudley, R.M.: On sequential convergence. Trans. Am. Math. Soc. 112, 483\u2013507 (1964)","journal-title":"Trans. Am. Math. Soc."},{"issue":"12","key":"1079_CR8","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(12), 1399\u20131419 (2011)","journal-title":"Optimization"},{"key":"1079_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/s11117-016-0412-6","author":"M Gaydu","year":"2016","unstructured":"Gaydu, M., Geoffroy, M.H., Jean-Alexis, C., Nedelcheva, D.: Stability of minimizers of set optimization problems. Positivity (2016). doi: 10.1007\/s11117-016-0412-6","journal-title":"Positivity"},{"key":"1079_CR10","doi-asserted-by":"crossref","unstructured":"Ha, T.X.D.: Optimality conditions for several types of efficient solutions of set-valued optimization problems. Nonlinear analysis and variational problems, vol. 35, pp. 305\u2013324, Springer Optim. Appl., Springer, New York (2010)","DOI":"10.1007\/978-1-4419-0158-3_21"},{"key":"1079_CR11","doi-asserted-by":"crossref","unstructured":"Holmes, R.B.: Geometric functional analysis and its applications. Graduate Texts in Mathematics, No. 24, pp. x+246. Springer-Verlag, New-York (1975)","DOI":"10.1007\/978-1-4684-9369-6"},{"key":"1079_CR12","doi-asserted-by":"crossref","unstructured":"Khan, A.A., Tammer, C., Z\u0103linescu, C.: Set-valued optimization. An introduction with applications. Vector Optimization. pp. xxii+765. Springer, Heidelberg (2015)","DOI":"10.1007\/978-3-642-54265-7"},{"issue":"2","key":"1079_CR13","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1007\/BF00122049","volume":"2","author":"B Lemaire","year":"1992","unstructured":"Lemaire, B.: Approximation in multiobjective optimization. J. Glob. Optim. 2(2), 117\u2013132 (1992)","journal-title":"J. Glob. Optim."},{"key":"1079_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-015-0802-0","author":"X-B Li","year":"2015","unstructured":"Li, X.-B., Wang, Q.-L., Lin, Z.: Stability of set-optimization problems with naturally quasi-functions. J. Optim. Theory Appl. (2015). doi: 10.1007\/s10957-015-0802-0","journal-title":"J. Optim. Theory Appl."},{"issue":"2","key":"1079_CR15","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1137\/110843125","volume":"50","author":"R L\u00f3pez","year":"2012","unstructured":"L\u00f3pez, R.: Approximations of equilibrium problems. SIAM J. Control Optim. 50(2), 1038\u20131070 (2012)","journal-title":"SIAM J. Control Optim."},{"issue":"1","key":"1079_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00186-013-0430-0","volume":"78","author":"R L\u00f3pez","year":"2013","unstructured":"L\u00f3pez, R.: Variational convergence for vector-valued functions and its applications to convex multiobjective optimization. Math. Meth. Oper. Res. 78(1), 1\u201334 (2013)","journal-title":"Math. Meth. Oper. Res."},{"issue":"2","key":"1079_CR17","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/BF00936165","volume":"43","author":"P Loridan","year":"1984","unstructured":"Loridan, P.: $$\\epsilon $$ \u03f5 -solutions in vector minimization problems. J. Optim. Theory Appl. 43(2), 265\u2013276 (1984)","journal-title":"J. Optim. Theory Appl."},{"key":"1079_CR18","doi-asserted-by":"crossref","unstructured":"Nieuwenhuis, J.W.: Separating sets with relative interior in Fr\u00e9chet spaces. Appl. Math. Optim. 3(4), 373\u2013376 (1976\/77)","DOI":"10.1007\/BF01448187"},{"issue":"4","key":"1079_CR19","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1007\/s10898-008-9284-z","volume":"42","author":"P Oppezzi","year":"2008","unstructured":"Oppezzi, P., Rossi, A.M.: A convergence for infinite dimensional vector valued functions. J. Glob. Optim. 42(4), 577\u2013586 (2008)","journal-title":"J. Glob. Optim."},{"issue":"2","key":"1079_CR20","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1007\/s10957-014-0669-5","volume":"165","author":"P Oppezzi","year":"2015","unstructured":"Oppezzi, P., Rossi, A.M.: Improvement sets and convergence of optimal points. J. Optim. Theory Appl. 165(2), 405\u2013419 (2015)","journal-title":"J. Optim. Theory Appl."},{"key":"1079_CR21","unstructured":"Peressini, A.L.: Ordered topological vector spaces. pp. x+228. Harper & Row, Publishers, New York (1967)"},{"key":"1079_CR22","doi-asserted-by":"crossref","unstructured":"Ponstein, J.: Approaches to the theory of optimization. Cambridge Tracts in Mathematics, vol. 77. pp. xii+205. Cambridge University Press, Cambridge (1980)","DOI":"10.1017\/CBO9780511526527"},{"key":"1079_CR23","doi-asserted-by":"crossref","unstructured":"Proinov, P.D.: A unified theory of cone metric spaces and its applications to the fixed point theory. Fixed Point Theory Appl. 103, 38 (2013)","DOI":"10.1186\/1687-1812-2013-103"},{"key":"1079_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-02431-3","volume-title":"Variational analysis, 317","author":"RT Rockafellar","year":"1998","unstructured":"Rockafellar, R.T., Wets, R.: Variational analysis, 317. Springer-Verlag, Berlin (1998)"},{"issue":"2","key":"1079_CR25","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/BF00940762","volume":"49","author":"DJ White","year":"1986","unstructured":"White, D.J.: Epsilon efficiency. J. Optim. Theory Appl. 49(2), 319\u2013337 (1986)","journal-title":"J. Optim. Theory Appl."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-016-1079-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-016-1079-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-016-1079-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,13]],"date-time":"2019-09-13T07:40:05Z","timestamp":1568360405000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-016-1079-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,12]]},"references-count":25,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2017,12]]}},"alternative-id":["1079"],"URL":"https:\/\/doi.org\/10.1007\/s11590-016-1079-4","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,9,12]]}}}