{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,19]],"date-time":"2023-08-19T20:45:40Z","timestamp":1692477940855},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,8,22]],"date-time":"2016-08-22T00:00:00Z","timestamp":1471824000000},"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":["J Optim Theory Appl"],"published-print":{"date-parts":[[2016,10]]},"DOI":"10.1007\/s10957-016-0995-x","type":"journal-article","created":{"date-parts":[[2016,8,22]],"date-time":"2016-08-22T16:25:06Z","timestamp":1471883106000},"page":"45-69","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Second-Order Conditions for Open-Cone Minimizers and Firm Minimizers in Set-Valued Optimization Subject to Mixed Constraints"],"prefix":"10.1007","volume":"171","author":[{"given":"Phan Quoc","family":"Khanh","sequence":"first","affiliation":[]},{"given":"Nguyen Minh","family":"Tung","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,8,22]]},"reference":[{"key":"995_CR1","volume-title":"On the Kuhn\u2013Tucker theorem in Nonlinear Programming (NATO Summer School, Menton, 1964)","author":"J Abadie","year":"1967","unstructured":"Abadie, J.: On the Kuhn\u2013Tucker theorem in Nonlinear Programming (NATO Summer School, Menton, 1964). North-Holland, Amsterdam (1967)"},{"key":"995_CR2","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1137\/S1052623496306760","volume":"9","author":"JF Bannans","year":"1999","unstructured":"Bannans, J.F., Cominetti, R., Shapiro, A.: Second order optimality conditions based on parabolic second order tangent sets. SIAM J. Optim. 9, 466\u2013492 (1999)","journal-title":"SIAM J. Optim."},{"key":"995_CR3","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/BF01445166","volume":"21","author":"R Cominetti","year":"1990","unstructured":"Cominetti, R.: Metric regularity, tangent sets, and second-order optimality conditions. Appl. Math. Optim. 21, 265\u2013287 (1990)","journal-title":"Appl. Math. Optim."},{"key":"995_CR4","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/s11228-012-0220-5","volume":"21","author":"H Gfrerer","year":"2013","unstructured":"Gfrerer, H.: On directional metric regularity, subregularity and optimality conditions for nonsmooth mathematical programs. Set-Valued Var. Anal. 21, 151\u2013176 (2013)","journal-title":"Set-Valued Var. Anal."},{"key":"995_CR5","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1137\/120891216","volume":"23","author":"H Gfrerer","year":"2013","unstructured":"Gfrerer, H.: On directional metric subregularity and second-order optimality conditions for a class of nonsmooth mathematical programs. SIAM J. Optim. 23, 632\u2013665 (2013)","journal-title":"SIAM J. Optim."},{"key":"995_CR6","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/BF01580754","volume":"41","author":"H Kawasaki","year":"1988","unstructured":"Kawasaki, H.: An envelope-like effect of infinitely many inequality constraints on second order necessary conditions for minimization problems. Math. Program. 41, 73\u201396 (1988)","journal-title":"Math. Program."},{"key":"995_CR7","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1137\/S0363012996311095","volume":"37","author":"JP Penot","year":"1999","unstructured":"Penot, J.P.: Second order conditions for optimization problems with constraints. SIAM J. Control Optim. 37, 303\u2013318 (1999)","journal-title":"SIAM J. Control Optim."},{"key":"995_CR8","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s10107-009-0318-1","volume":"123","author":"C Guti\u00e9rrez","year":"2010","unstructured":"Guti\u00e9rrez, C., Jim\u00e9nez, B., Novo, N.: On second order Fritz John type optimality conditions in nonsmooth multiobjective programming. Math. Program. Ser. B 123, 199\u2013223 (2010)","journal-title":"Math. Program. Ser. B"},{"key":"995_CR9","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s00245-003-0782-6","volume":"49","author":"B Jim\u00e9nez","year":"2004","unstructured":"Jim\u00e9nez, B., Novo, V.: Optimality conditions in differentiable vector optimization via second-order tangent sets. Appl. Math. Optim. 49, 123\u2013144 (2004)","journal-title":"Appl. Math. Optim."},{"key":"995_CR10","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/s10957-007-9169-1","volume":"133","author":"PQ Khanh","year":"2007","unstructured":"Khanh, P.Q., Tuan, N.D.: Optimality conditions for nonsmooth multiobjective optimization using Hadamard directional derivatives. J. Optim. Theory Appl. 133, 341\u2013357 (2007)","journal-title":"J. Optim. Theory Appl."},{"key":"995_CR11","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1016\/j.jmaa.2012.12.075","volume":"403","author":"PQ Khanh","year":"2013","unstructured":"Khanh, P.Q., Tuan, N.D.: Second order optimality conditions with the envelope-like effect in nonsmooth multiobjective programming II: optimality conditions. J. Math. Anal. Appl. 403, 703\u2013714 (2013)","journal-title":"J. Math. Anal. Appl."},{"key":"995_CR12","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.na.2012.09.013","volume":"77","author":"PQ Khanh","year":"2013","unstructured":"Khanh, P.Q., Tuan, N.D.: Second-order optimality conditions with the envelope-like effect for nonsmooth vector optimization in infinite dimensions. Nonlinear Anal. 77, 130\u2013148 (2013)","journal-title":"Nonlinear Anal."},{"key":"995_CR13","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s10898-010-9580-2","volume":"50","author":"A Taa","year":"2011","unstructured":"Taa, A.: Second order conditions for nonsmooth multiobjective optimization problems with inclusion constraints. J. Glob. Optim. 50, 271\u2013291 (2011)","journal-title":"J. Glob. Optim."},{"key":"995_CR14","doi-asserted-by":"crossref","first-page":"4816","DOI":"10.1016\/j.amc.2012.10.107","volume":"219","author":"S Zhu","year":"2013","unstructured":"Zhu, S., Li, S.: Optimality conditions of strict minimality in optimization problems under inclusion constraints. Appl. Math. Comput. 219, 4816\u20134825 (2013)","journal-title":"Appl. Math. Comput."},{"key":"995_CR15","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s10957-007-9179-z","volume":"133","author":"M Durea","year":"2007","unstructured":"Durea, M.: First and second order Lagrange claims for set-valued maps. J. Optim. Theory Appl. 133, 111\u2013116 (2007)","journal-title":"J. Optim. Theory Appl."},{"key":"995_CR16","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s10957-004-1841-0","volume":"125","author":"J Jahn","year":"2005","unstructured":"Jahn, J., Khan, A.A., Zeilinger, P.: Second-order optimality conditions in set optimization. J. Optim. Theory Appl. 125, 331\u2013347 (2005)","journal-title":"J. Optim. Theory Appl."},{"key":"995_CR17","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1007\/s10957-012-0076-8","volume":"155","author":"SJ Li","year":"2012","unstructured":"Li, S.J., Zhu, S.K., Li, X.B.: Second order optimality conditions for strict efficiency of constrained set-valued optimization. J. Optim. Theory Appl. 155, 534\u2013557 (2012)","journal-title":"J. Optim. Theory Appl."},{"key":"995_CR18","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1080\/02331934.2012.674948","volume":"62","author":"AA Khan","year":"2013","unstructured":"Khan, A.A., Tammer, C.: Second-order optimality conditions in set-valued optimization via asymptotic derivatives. Optimization 62, 743\u2013758 (2013)","journal-title":"Optimization"},{"key":"995_CR19","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1007\/s10898-013-0067-9","volume":"58","author":"SK Zhu","year":"2014","unstructured":"Zhu, S.K., Li, S.J., Teo, K.L.: Second-order Karush\u2013Kuhn\u2013Tucker optimality conditions for set-valued optimization. J. Glob. Optim. 58, 673\u2013679 (2014)","journal-title":"J. Glob. Optim."},{"key":"995_CR20","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1007\/s11117-015-0330-z","volume":"19","author":"PQ Khanh","year":"2015","unstructured":"Khanh, P.Q., Tung, N.M.: First and second-order optimality conditions without differentiability in multivalued vector optimization. Positivity 19, 817\u2013841 (2015)","journal-title":"Positivity"},{"key":"995_CR21","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/s10957-015-0728-6","volume":"167","author":"PQ Khanh","year":"2015","unstructured":"Khanh, P.Q., Tung, N.M.: Second-order optimality conditions with the envelope-like effect for set-valued optimization. J. Optim. Theory Appl. 167, 68\u201390 (2015)","journal-title":"J. Optim. Theory Appl."},{"key":"995_CR22","doi-asserted-by":"crossref","first-page":"1044","DOI":"10.1137\/0324061","volume":"24","author":"M Studniarski","year":"1986","unstructured":"Studniarski, M.: Necessary and sufficient conditions for isolated local minima of nonsmooth functions. SIAM J. Control Optim. 24, 1044\u20131049 (1986)","journal-title":"SIAM J. Control Optim."},{"key":"995_CR23","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1006\/jmaa.2001.7588","volume":"265","author":"B Jim\u00e9nez","year":"2002","unstructured":"Jim\u00e9nez, B.: Strict efficiency in vector optimization. J. Math. Anal. Appl. 265, 264\u2013284 (2002)","journal-title":"J. Math. Anal. Appl."},{"key":"995_CR24","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1137\/07070139X","volume":"48","author":"F Flores-Baz\u00e1n","year":"2009","unstructured":"Flores-Baz\u00e1n, F., Jim\u00e9nez, B.: Strict efficiency in set-valued optimization. SIAM J. Control Optim. 48, 881\u2013908 (2009)","journal-title":"SIAM J. Control Optim."},{"key":"995_CR25","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1137\/0322033","volume":"22","author":"JP Penot","year":"1984","unstructured":"Penot, J.P.: Differentiability of relations and differential stability of perturbed optimization problems. SIAM J. Control Optim. 22, 529\u2013551 (1984)","journal-title":"SIAM J. Control Optim."},{"key":"995_CR26","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/j.jmaa.2008.07.041","volume":"348","author":"DE Ward","year":"2008","unstructured":"Ward, D.E.: A chain rule for first and second order epiderivatives and hypoderivatives. J. Math. Anal. Appl. 348, 324\u2013336 (2008)","journal-title":"J. Math. Anal. Appl."},{"key":"995_CR27","volume-title":"Set-Valued Optimization: An Introduction with Application","author":"AA Khan","year":"2014","unstructured":"Khan, A.A., Tammer, C., Zalinescu, C.: Set-Valued Optimization: An Introduction with Application. Springer, Berlin (2014)"},{"key":"995_CR28","volume-title":"Set-Valued Analysis","author":"JP Aubin","year":"1990","unstructured":"Aubin, J.P., Frankowska, H.: Set-Valued Analysis. Birkhauser, Boston (1990)"},{"key":"995_CR29","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-31247-1","volume-title":"Variational Analysis and Generalized Differentiation, Applications","author":"BS Mordukhovich","year":"2006","unstructured":"Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, Applications, vol. II. Springer, Berlin (2006)"},{"key":"995_CR30","volume-title":"Variational Analysis","author":"RT Rockafellar","year":"2009","unstructured":"Rockafellar, R.T., Wets, R.J.B.: Variational Analysis, 3rd edn. Springer, Berlin (2009)","edition":"3"},{"key":"995_CR31","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-87821-8","volume-title":"Implicit Functions and Solution Mappings","author":"AL Dontchev","year":"2009","unstructured":"Dontchev, A.L., Rockafellar, R.T.: Implicit Functions and Solution Mappings. Springer, Berlin (2009)"},{"key":"995_CR32","doi-asserted-by":"crossref","first-page":"2561","DOI":"10.1137\/140991157","volume":"25","author":"PQ Khanh","year":"2015","unstructured":"Khanh, P.Q., Kruger, A.K., Thao, N.H.: An induction theorem and nonlinear regularity models. SIAM J. Optim. 25, 2561\u20132588 (2015)","journal-title":"SIAM J. Optim."},{"key":"995_CR33","first-page":"305","volume-title":"Chapter 21, Nonlinear Analysis and Variational Problems","author":"TXD Ha","year":"2009","unstructured":"Ha, T.X.D.: Optimality conditions for several types of efficient solutions of set-valued optimization problems. In: Pardalos, P., Rassis, ThM, Khan, A.A. (eds.) Chapter 21, Nonlinear Analysis and Variational Problems, pp. 305\u2013324. Springer, Heidelberg (2009)"},{"key":"995_CR34","doi-asserted-by":"crossref","DOI":"10.1142\/5021","volume-title":"Convex Analysis in General Vector Spaces","author":"C Zalinescu","year":"2002","unstructured":"Zalinescu, C.: Convex Analysis in General Vector Spaces. World Scientific, New Jersey\/London (2002)"},{"key":"995_CR35","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1287\/moor.1.2.130","volume":"1","author":"SM Robinson","year":"1976","unstructured":"Robinson, S.M.: Regularity and stability for convex multivalued functions. Math. Oper. Res. 1, 130\u2013143 (1976)","journal-title":"Math. Oper. Res."},{"key":"995_CR36","doi-asserted-by":"crossref","first-page":"438","DOI":"10.21136\/CMJ.1975.101337","volume":"25","author":"C Ursescu","year":"1975","unstructured":"Ursescu, C.: Multifunctions with closed convex graph. Czechoslov. Math. J. 25, 438\u2013441 (1975)","journal-title":"Czechoslov. Math. J."},{"key":"995_CR37","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03271-8","volume-title":"Introduction to the Theory of Nonlinear Optimization","author":"J Jahn","year":"1996","unstructured":"Jahn, J.: Introduction to the Theory of Nonlinear Optimization, 2nd edn. Springer, Berlin (1996)","edition":"2"},{"key":"995_CR38","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1137\/0713043","volume":"13","author":"SM Robinson","year":"1976","unstructured":"Robinson, S.M.: Stability theorems for systems of inequalities. Part II: Differentiable nonlinear systems. SIAM J. Numer. Anal. 13, 497\u2013513 (1976)","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-016-0995-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-016-0995-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-016-0995-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,19]],"date-time":"2023-08-19T20:08:02Z","timestamp":1692475682000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-016-0995-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,22]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,10]]}},"alternative-id":["995"],"URL":"https:\/\/doi.org\/10.1007\/s10957-016-0995-x","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,8,22]]}}}