{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:20:51Z","timestamp":1762323651408},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,11,9]],"date-time":"2013-11-09T00:00:00Z","timestamp":1383955200000},"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":[[2014,7]]},"DOI":"10.1007\/s10957-013-0469-3","type":"journal-article","created":{"date-parts":[[2013,11,8]],"date-time":"2013-11-08T11:28:18Z","timestamp":1383910098000},"page":"1-12","source":"Crossref","is-referenced-by-count":3,"title":["Weak Subdifferentials for Set-Valued Mappings"],"prefix":"10.1007","volume":"162","author":[{"given":"X. J.","family":"Long","sequence":"first","affiliation":[]},{"given":"J. W.","family":"Peng","sequence":"additional","affiliation":[]},{"given":"X. B.","family":"Li","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,11,9]]},"reference":[{"key":"469_CR1","volume-title":"Convex Analysis","author":"R.T. Rockafellar","year":"1979","unstructured":"Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1979)"},{"key":"469_CR2","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/s001860050021","volume":"48","author":"G.Y. Chen","year":"1998","unstructured":"Chen, G.Y., Jahn, J.: Optimality conditions for set-valued optimization problems. Math. Methods Oper. Res. 48, 187\u2013200 (1998)","journal-title":"Math. Methods Oper. Res."},{"key":"469_CR3","volume-title":"Set-Valued Analysis","author":"J.P. Aubin","year":"1990","unstructured":"Aubin, J.P., Frankowska, H.: Set-Valued Analysis. Birkh\u00e4user, Boston (1990)"},{"key":"469_CR4","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1023\/A:1021733402240","volume":"100","author":"J. Baier","year":"1999","unstructured":"Baier, J., Jahn, J.: On subdifferentials of set-valued maps. J. Optim. Theory Appl. 100, 233\u2013240 (1999)","journal-title":"J. Optim. Theory Appl."},{"key":"469_CR5","doi-asserted-by":"crossref","first-page":"189","DOI":"10.7146\/math.scand.a-11911","volume":"48","author":"J.M. Borwein","year":"1981","unstructured":"Borwein, J.M.: A Lagrange multiplier theorem and a sandwich theorem for convex relations. Math. Scand. 48, 189\u2013204 (1981)","journal-title":"Math. Scand."},{"key":"469_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-24828-6","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":"469_CR7","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1080\/0233193031000120051","volume":"52","author":"W. Song","year":"2003","unstructured":"Song, W.: Weak subdifferential of set-valued mappings. Optimization 52, 263\u2013276 (2003)","journal-title":"Optimization"},{"key":"469_CR8","doi-asserted-by":"crossref","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, 84\u201397 (1992)","journal-title":"J. Math. Anal. Appl."},{"key":"469_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01415945","volume":"34","author":"G.Y. Chen","year":"1990","unstructured":"Chen, G.Y., Craven, B.D.: A vector variational inequality and optimization over an efficient set. Math. Methods Oper. Res. 34, 1\u201312 (1990)","journal-title":"Math. Methods Oper. Res."},{"key":"469_CR10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/02331939208843803","volume":"25","author":"X.Q. Yang","year":"1992","unstructured":"Yang, X.Q.: A Hahn\u2013Banach theorem in ordered linear spaces and its applications. Optimization 25, 1\u20139 (1992)","journal-title":"Optimization"},{"key":"469_CR11","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s001860400397","volume":"61","author":"W.J. Peng","year":"2005","unstructured":"Peng, W.J., Lee, H.W.J., Rong, W.D., Yang, X.M.: Hahn-Banach theorems and subgradients of set-valued maps. Math. Methods Oper. Res. 61, 281\u2013297 (2005)","journal-title":"Math. Methods Oper. Res."},{"key":"469_CR12","doi-asserted-by":"crossref","first-page":"5781","DOI":"10.1016\/j.na.2009.04.065","volume":"71","author":"S.J. Li","year":"2009","unstructured":"Li, S.J., Guo, X.L.: Weak subdifferential for set-valued mappings and it applications. Nonlinear Anal. 71, 5781\u20135789 (2009)","journal-title":"Nonlinear Anal."},{"key":"469_CR13","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1007\/s00186-007-0193-6","volume":"68","author":"C. Zalinescu","year":"2008","unstructured":"Zalinescu, C.: Hahn-Banach extension theorems for multifunctions revisited. Math. Methods Oper. Res. 68, 493\u2013508 (2008)","journal-title":"Math. Methods Oper. Res."},{"key":"469_CR14","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1007\/s10957-010-9787-x","volume":"149","author":"E. Hernandez","year":"2011","unstructured":"Hernandez, E., Rodriguez-Marin, L.: Weak and strong subgradients of set-valued maps. J. Optim. Theory Appl. 149, 352\u2013365 (2011)","journal-title":"J. Optim. Theory Appl."},{"key":"469_CR15","doi-asserted-by":"crossref","first-page":"215","DOI":"10.4064\/fm-15-1-215-218","volume":"15","author":"G. Bouligand","year":"1930","unstructured":"Bouligand, G.: Sur l\u2019existence des demi-tangentes \u00e1 une courbe de Jordan. Fundam. Math. 15, 215 (1930)","journal-title":"Fundam. Math."},{"key":"469_CR16","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1080\/02331939608844169","volume":"36","author":"A. Taa","year":"1996","unstructured":"Taa, A.: Necessary and sufficient conditions for multiobjective optimization problems. Optimization 36, 97\u2013104 (1996)","journal-title":"Optimization"},{"key":"469_CR17","doi-asserted-by":"crossref","first-page":"1293","DOI":"10.1080\/01630569508816674","volume":"16","author":"T. Amahroq","year":"1995","unstructured":"Amahroq, T., Thibault, L.: On proto-differentiability and strict proto-differentiability of multifunctions of feasible points in perturbed optimization problems. Numer. Funct. Anal. Optim. 16, 1293\u20131307 (1995)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"469_CR18","first-page":"109","volume":"4","author":"W.W. 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":"469_CR19","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1080\/01630569808816819","volume":"19","author":"A. Taa","year":"1998","unstructured":"Taa, A.: Set-valued derivatives of multifunctions and optimality conditions. Numer. Funct. Anal. Optim. 19, 121\u2013149 (1998)","journal-title":"Numer. Funct. Anal. Optim."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-013-0469-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-013-0469-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-013-0469-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,1]],"date-time":"2019-08-01T03:08:27Z","timestamp":1564628907000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-013-0469-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,9]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,7]]}},"alternative-id":["469"],"URL":"https:\/\/doi.org\/10.1007\/s10957-013-0469-3","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,9]]}}}