{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T21:34:43Z","timestamp":1763415283227},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2012,3,13]],"date-time":"2012-03-13T00:00:00Z","timestamp":1331596800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2013,8]]},"DOI":"10.1007\/s11590-012-0463-y","type":"journal-article","created":{"date-parts":[[2012,3,12]],"date-time":"2012-03-12T09:39:34Z","timestamp":1331545174000},"page":"1087-1117","source":"Crossref","is-referenced-by-count":18,"title":["Normal subdifferentials of efficient point multifunctions in parametric vector optimization"],"prefix":"10.1007","volume":"7","author":[{"given":"Thai Doan","family":"Chuong","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,3,13]]},"reference":[{"key":"463_CR1","first-page":"159","volume-title":"Mathematical Analysis and Applications","author":"J.P. Aubin","year":"1981","unstructured":"Aubin J.P.: Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions. In: Nachbin, L. (eds) Mathematical Analysis and Applications, pp. 159\u2013229. Academic Press, New York (1981)"},{"issue":"2","key":"463_CR2","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/s10957-007-9209-x","volume":"135","author":"T.Q. Bao","year":"2007","unstructured":"Bao T.Q., Gupta P., Mordukhovich B.S.: Necessary conditions in multiobjective optimization with equilibrium constraints. J. Optim. Theory Appl. 135(2), 179\u2013203 (2007)","journal-title":"J. Optim. Theory Appl."},{"key":"463_CR3","first-page":"531","volume":"36","author":"T.Q. Bao","year":"2007","unstructured":"Bao T.Q., Mordukhovich B.S.: Variational principles for set-valued mappings with applications to multiobjective optimization. Control Cyber. 36, 531\u2013562 (2007)","journal-title":"Control Cyber."},{"issue":"4","key":"463_CR4","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1007\/s10898-008-9336-4","volume":"43","author":"T.Q. Bao","year":"2009","unstructured":"Bao T.Q., Mordukhovich B.S.: Necessary conditions for super minimizers in constrained multiobjective optimization. J. Global Optim. 43(4), 533\u2013552 (2009)","journal-title":"J. Global Optim."},{"key":"463_CR5","first-page":"375","volume":"27","author":"E.M. Bednarczuk","year":"1998","unstructured":"Bednarczuk E.M., Song W.: Contingent epiderivate and its applications to set-valued maps. Control Cybernet. 27, 375\u2013386 (1998)","journal-title":"Control Cybernet."},{"key":"463_CR6","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s10479-007-0186-0","volume":"154","author":"A. Chinchuluun","year":"2007","unstructured":"Chinchuluun A., Pardalos P.M.: A survey of recent developments in multiobjective optimization. Ann. Oper. Res. 154, 29\u201350 (2007)","journal-title":"Ann. Oper. Res."},{"key":"463_CR7","volume-title":"Pareto Optimality, Game Theory and Equilibria","year":"2008","unstructured":"Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L. (eds): Pareto Optimality, Game Theory and Equilibria. Springer, Berlin (2008)"},{"key":"463_CR8","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/j.na.2010.08.042","volume":"74","author":"T.D. Chuong","year":"2011","unstructured":"Chuong T.D.: Clarke coderivatives of efficient point multifunctions in parametric vector optimization. Nonlinear Anal. 74, 273\u2013285 (2011)","journal-title":"Nonlinear Anal."},{"key":"463_CR9","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1007\/s10898-008-9391-x","volume":"45","author":"T.D. Chuong","year":"2009","unstructured":"Chuong T.D., Huy N.Q., Yao J.-C.: Stability of semi-infinite vector optimization problems under functional purtubations. J. Global Optim. 45, 583\u2013595 (2009)","journal-title":"J. Global Optim."},{"key":"463_CR10","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1016\/j.ejor.2009.01.004","volume":"200","author":"T.D. Chuong","year":"2010","unstructured":"Chuong T.D., Huy N.Q., Yao J.-C.: Pseudo-Lipschitz property of linear semi-infinite vector optimization problems. Eur. J. Oper. Res. 200, 639\u2013644 (2010)","journal-title":"Eur. J. Oper. Res."},{"key":"463_CR11","doi-asserted-by":"crossref","first-page":"1462","DOI":"10.1137\/080737083","volume":"20","author":"T.D. Chuong","year":"2009","unstructured":"Chuong T.D., Huy N.Q., Yao J.-C.: Subdifferentials of marginal functions in semi-infinite programming. SIAM J. Optim. 20, 1462\u20131477 (2009)","journal-title":"SIAM J. Optim."},{"key":"463_CR12","doi-asserted-by":"crossref","first-page":"6312","DOI":"10.1016\/j.na.2009.06.038","volume":"71","author":"T.D. Chuong","year":"2009","unstructured":"Chuong T.D., Yao J.-C.: Sufficient conditions for pseudo-Lipschitz property in convex semi-infinite vector optimization problems. Nonlinear Anal. 71, 6312\u20136322 (2009)","journal-title":"Nonlinear Anal."},{"key":"463_CR13","doi-asserted-by":"crossref","first-page":"1671","DOI":"10.11650\/twjm\/1500405608","volume":"13","author":"T.D. Chuong","year":"2009","unstructured":"Chuong T.D., Yao J.-C.: Coderivatives of efficient point multifunctions in parametric vector optimization. Taiwan. J. Math. 13, 1671\u20131693 (2009)","journal-title":"Taiwan. J. Math."},{"key":"463_CR14","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/s10957-010-9646-9","volume":"146","author":"T.D. Chuong","year":"2010","unstructured":"Chuong T.D., Yao J.-C.: Generalized Clarke epiderivatives of parametric vector optimization problems. J. Optim. Theory Appl. 146, 77\u201394 (2010)","journal-title":"J. Optim. Theory Appl."},{"key":"463_CR15","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1051\/cocv:2007027","volume":"13","author":"N. Dinh","year":"2007","unstructured":"Dinh N., Goberna M.A., L\u00f3pez M.A., Son T.Q.: New Farkas-type constraint qualifications in convex infinite programming. ESAIM Control Optim. Calc. Var. 13, 580\u2013597 (2007)","journal-title":"ESAIM Control Optim. Calc. Var."},{"key":"463_CR16","first-page":"123","volume":"34","author":"N. Dinh","year":"2009","unstructured":"Dinh N., Mordukhovich B.S., Nghia T.T.A.: Qualification and optimality conditions for DC programs with infinite constraints. Acta Math. Vietnam. 34, 123\u2013153 (2009)","journal-title":"Acta Math. Vietnam."},{"key":"463_CR17","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/s10107-009-0323-4","volume":"123","author":"N. Dinh","year":"2010","unstructured":"Dinh N., Mordukhovich B.S., Nghia T.T.A.: Subifferentials of value functions and optimality conditions for some classes of DC and bilevel infinite and semi-infinite programs. Math. Program. 123, 101\u2013138 (2010)","journal-title":"Math. Program."},{"key":"463_CR18","volume-title":"Linear Semi-Infinite Optimization","author":"M.A. Goberna","year":"1998","unstructured":"Goberna M.A., L\u00f3pez M.A.: Linear Semi-Infinite Optimization. Wiley, Chichester (1998)"},{"key":"463_CR19","volume-title":"Theory of Extremal Problems","author":"A.D. Ioffe","year":"1979","unstructured":"Ioffe A.D., Tihomirov V.M.: Theory of Extremal Problems. North-Holland, Amsterdam (1979)"},{"issue":"8","key":"463_CR20","doi-asserted-by":"crossref","first-page":"2083","DOI":"10.11650\/twjm\/1500405137","volume":"12","author":"N.Q. Huy","year":"2008","unstructured":"Huy N.Q., Mordukhovich B.S., Yao J.-C.: Coderivatives of frontier and solution maps in parametric multiobjective optimization. Taiwan. J. Math. 12(8), 2083\u20132111 (2008)","journal-title":"Taiwan. J. Math."},{"issue":"3","key":"463_CR21","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1007\/BF02275356","volume":"89","author":"H. Kuk","year":"1996","unstructured":"Kuk H., Tanino T., Tanaka M.: Sensitivity analysis in vector optimization. J. Optim. Theory Appl. 89(3), 713\u2013730 (1996)","journal-title":"J. Optim. Theory Appl."},{"issue":"3","key":"463_CR22","doi-asserted-by":"crossref","first-page":"945","DOI":"10.11650\/twjm\/1500404767","volume":"11","author":"G.M. Lee","year":"2007","unstructured":"Lee G.M., Huy N.Q.: On sensitivity analysis in vector optimization. Taiwan. J. Math. 11(3), 945\u2013958 (2007)","journal-title":"Taiwan. J. Math."},{"issue":"1","key":"463_CR23","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1137\/060676982","volume":"19","author":"C. Li","year":"2008","unstructured":"Li C., Ng K.F., Pong T.K.: Constraint qualifications for convex inequality systems with applications in constrained optimization. SIAM J. Optim. 19(1), 163\u2013187 (2008)","journal-title":"SIAM J. Optim."},{"key":"463_CR24","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1007\/s11228-010-0171-7","volume":"19","author":"S. Li","year":"2011","unstructured":"Li S., Penot J.-P., Xue X.: Codifferential calculus. Set Valued Var. Anal. 19, 505\u2013536 (2011)","journal-title":"Set Valued Var. Anal."},{"key":"463_CR25","first-page":"526","volume":"22","author":"B.S. Mordukhovich","year":"1980","unstructured":"Mordukhovich B.S.: Metric approximations and necessary optimality conditions for general classes of nonsmooth extremal problems. Soviet Math. Dokl. 22, 526\u2013530 (1980)","journal-title":"Soviet Math. Dokl."},{"key":"463_CR26","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s10107-007-0172-y","volume":"117","author":"B.S. Mordukhovich","year":"2009","unstructured":"Mordukhovich B.S.: Multiobjective optimization problems with equilibrium constraints. Math. Progr. Ser. B 117, 331\u2013354 (2009)","journal-title":"Math. Progr. Ser. B"},{"key":"463_CR27","volume-title":"Variational Analysis and Generalized Differentiation. I: Basic Theory","author":"B.S. Mordukhovich","year":"2006","unstructured":"Mordukhovich B.S.: Variational Analysis and Generalized Differentiation. I: Basic Theory. Springer, Berlin (2006)"},{"key":"463_CR28","volume-title":"Variational Analysis and Generalized Differentiation. II: Applications","author":"B.S. Mordukhovich","year":"2006","unstructured":"Mordukhovich B.S.: Variational Analysis and Generalized Differentiation. II: Applications. Springer, Berlin (2006)"},{"key":"463_CR29","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/s10107-007-0120-x","volume":"116","author":"B.S. Mordukhovich","year":"2009","unstructured":"Mordukhovich B.S., Nam N.M., Yen N.D.: Subgradients of marginal functions in parametric mathematical programming. Math. Progr. Ser. B 116, 369\u2013396 (2009)","journal-title":"Math. Progr. Ser. B"},{"key":"463_CR30","first-page":"400","volume":"93","author":"J.-P. Pennot","year":"1983","unstructured":"Pennot J.-P.: Compact nets, filters, and relations. J. Optim. Theory Appl. 93, 400\u2013417 (1983)","journal-title":"J. Optim. Theory Appl."},{"key":"463_CR31","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1007\/BFb0120850","volume":"10","author":"S.M. Robinson","year":"1979","unstructured":"Robinson S.M.: Generalized equations and their solutions, part i: basic theory. Math. Progr. Study 10, 128\u2013141 (1979)","journal-title":"Math. Progr. Study"},{"issue":"1","key":"463_CR32","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/BF00940783","volume":"77","author":"D.S. Shi","year":"1993","unstructured":"Shi D.S.: Sensitivity analysis in convex vector optimization. J. Optim. Theory Appl. 77(1), 145\u2013159 (1993)","journal-title":"J. Optim. Theory Appl."},{"key":"463_CR33","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF00939554","volume":"56","author":"T. Tanino","year":"1988","unstructured":"Tanino T.: Sensitivity analysis in multiobjective optimization. J. Optim. Theory Appl. 56, 479\u2013499 (1988)","journal-title":"J. Optim. Theory Appl."},{"key":"463_CR34","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1137\/0326031","volume":"26","author":"T. Tanino","year":"1988","unstructured":"Tanino T.: Stability and sensitivity analysis in convex vector optimization. SIAM J. Control Optim. 26, 521\u2013536 (1988)","journal-title":"SIAM J. Control Optim."},{"issue":"2","key":"463_CR35","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1016\/j.jmaa.2005.08.093","volume":"321","author":"D. Yuan","year":"2006","unstructured":"Yuan D., Chinchuluun A., Liu X., Pardalos P.M.: Generalized convexities and generalized gradients based on algebraic operations. J. Math. Anal. Appl. 321(2), 675\u2013690 (2006)","journal-title":"J. Math. Anal. Appl."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-012-0463-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-012-0463-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-012-0463-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,25]],"date-time":"2019-06-25T05:17:20Z","timestamp":1561439840000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-012-0463-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,13]]},"references-count":35,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2013,8]]}},"alternative-id":["463"],"URL":"https:\/\/doi.org\/10.1007\/s11590-012-0463-y","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3,13]]}}}