{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T18:09:01Z","timestamp":1770487741778,"version":"3.49.0"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2016,9,30]],"date-time":"2016-09-30T00:00:00Z","timestamp":1475193600000},"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":["Ann Oper Res"],"published-print":{"date-parts":[[2018,8]]},"DOI":"10.1007\/s10479-016-2337-7","type":"journal-article","created":{"date-parts":[[2016,9,30]],"date-time":"2016-09-30T02:56:48Z","timestamp":1475204208000},"page":"81-99","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Normal regularity for the feasible set of semi-infinite multiobjective optimization problems with applications"],"prefix":"10.1007","volume":"267","author":[{"given":"Thai Doan","family":"Chuong","sequence":"first","affiliation":[]},{"given":"Do Sang","family":"Kim","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,9,30]]},"reference":[{"key":"2337_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1394-9","volume-title":"Perturbation analysis of optimization problems","author":"JF Bonnans","year":"2000","unstructured":"Bonnans, J. F., & Shapiro, A. (2000). Perturbation analysis of optimization problems. New York: Springer."},{"key":"2337_CR2","doi-asserted-by":"crossref","first-page":"1504","DOI":"10.1137\/090765948","volume":"20","author":"MJ Canovas","year":"2009","unstructured":"Canovas, M. J., Lopez, M. A., Mordukhovich, B. S., & Parra, J. (2009). Variational analysis in semi-infinite and infinite programming. I. Stability of linear inequality systems of feasible solutions. SIAM Journal on Optimization, 20, 1504\u20131526.","journal-title":"SIAM Journal on Optimization"},{"key":"2337_CR3","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s10957-012-0099-1","volume":"156","author":"TD Chuong","year":"2013","unstructured":"Chuong, T. D. (2013). Derivatives of the efficient point multifunction in parametric vector optimization problems. Journal of Optimization Theory and Applications, 156, 247\u2013265.","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"2","key":"2337_CR4","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1016\/j.orl.2016.02.003","volume":"44","author":"TD Chuong","year":"2016","unstructured":"Chuong, T. D. (2016). Nondifferentiable fractional semi-infinite multiobjective optimization problems. Operations Research Letters, 44(2), 260\u2013266.","journal-title":"Operations Research Letters"},{"key":"2337_CR5","doi-asserted-by":"crossref","first-page":"1462","DOI":"10.1137\/080737083","volume":"20","author":"TD Chuong","year":"2009","unstructured":"Chuong, T. D., Huy, N. Q., & Yao, J.-C. (2009). Subdifferentials of marginal functions in semi-infinite programming. SIAM Journal on Optimization, 20, 1462\u20131477.","journal-title":"SIAM Journal on Optimization"},{"key":"2337_CR6","doi-asserted-by":"crossref","unstructured":"Chuong, T. D., & Kim, D. S. (2014a). Nonsmooth semi-infinite multiobjective optimization problems. Journal of Optimization Theory and Applications, 160, 748\u2013762.","DOI":"10.1007\/s10957-013-0314-8"},{"key":"2337_CR7","doi-asserted-by":"crossref","unstructured":"Chuong, T. D., & Kim, D. S. (2014b). Optimality conditions and duality in nonsmooth multiobjective optimization problems. Annals of Operations Research, 217, 117\u2013136.","DOI":"10.1007\/s10479-014-1552-3"},{"key":"2337_CR8","doi-asserted-by":"publisher","unstructured":"Chuong, T. D., & Kim, D. S. (2015). Nondifferentiable minimax programming problems with applications. Annals of Operations Research. doi: 10.1007\/s10479-015-1843-3 .","DOI":"10.1007\/s10479-015-1843-3"},{"issue":"2","key":"2337_CR9","doi-asserted-by":"crossref","first-page":"596","DOI":"10.1287\/moor.2015.0741","volume":"41","author":"TD Chuong","year":"2016","unstructured":"Chuong, T. D., & Kim, D. S. (2016). Holder-like property and metric regularity of a positive-order for implicit multifunctions. Mathematics of Operations Research, 41(2), 596\u2013611.","journal-title":"Mathematics of Operations Research"},{"key":"2337_CR10","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/s10957-010-9646-9","volume":"146","author":"TD Chuong","year":"2010","unstructured":"Chuong, T. D., & Yao, J.-C. (2010). Generalized Clarke epiderivatives of parametric vector optimization problems. Journal of Optimization Theory and Applications, 146, 77\u201394.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"2337_CR11","volume-title":"Optimization and nonsmooth analysis","author":"FH Clarke","year":"1983","unstructured":"Clarke, F. H. (1983). Optimization and nonsmooth analysis. New York: Wiley."},{"key":"2337_CR12","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. (2007). New Farkas-type constraint qualifications in convex infinite programming. ESAIM: Control, Optimisation and Calculus of Variations, 13, 580\u2013597.","journal-title":"ESAIM: Control, Optimisation and Calculus of Variations"},{"key":"2337_CR13","first-page":"123","volume":"34","author":"N Dinh","year":"2009","unstructured":"Dinh, N., Mordukhovich, B. S., & Nghia, T. T. A. (2009). Qualification and optimality conditions for DC programs with infinite constraints. Acta Mathematica Vietnamica, 34, 123\u2013153.","journal-title":"Acta Mathematica Vietnamica"},{"key":"2337_CR14","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. (2010). Subifferentials of value functions and optimality conditions for some classes of DC and bilevel infinite and semi-infinite programs. Mathematical Programming, 123, 101\u2013138.","journal-title":"Mathematical Programming"},{"key":"2337_CR15","volume-title":"Linear semi-infinite optimization","author":"MA Goberna","year":"1998","unstructured":"Goberna, M. A., & L\u00f3pez, M. A. (1998). Linear semi-infinite optimization. Chichester: Wiley."},{"key":"2337_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-8044-1","volume-title":"Post-optimal analysis in linear semi-infinite optimization","author":"MA Goberna","year":"2014","unstructured":"Goberna, M. A., & L\u00f3pez, M. A. (2014). Post-optimal analysis in linear semi-infinite optimization. New York: Springer."},{"key":"2337_CR17","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s00245-011-9152-y","volume":"65","author":"NQ Huy","year":"2012","unstructured":"Huy, N. Q., Giang, N. D., & Yao, J.-C. (2012). Subdifferential of optimal value functions in nonlinear infinite programming. Applied Mathematics and Optimization, 65, 91\u2013109.","journal-title":"Applied Mathematics and Optimization"},{"issue":"2","key":"2337_CR18","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1137\/060652087","volume":"18","author":"C Li","year":"2007","unstructured":"Li, C., Ng, K. F., & Pong, T. K. (2007). The SECQ, linear regularity, and the strong CHIP for an infinite system of closed convex sets in normed linear spaces. SIAM Journal on Optimization, 18(2), 643\u2013665.","journal-title":"SIAM Journal on Optimization"},{"issue":"1","key":"2337_CR19","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. (2008). Constraint qualifications for convex inequality systems with applications in constrained optimization. SIAM Journal on Optimization, 19(1), 163\u2013187.","journal-title":"SIAM Journal on Optimization"},{"key":"2337_CR20","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-50280-4","volume-title":"Theory of vector optimization","author":"DT Luc","year":"1989","unstructured":"Luc, D. T. (1989). Theory of vector optimization. Berlin: Springer."},{"key":"2337_CR21","volume-title":"Variational analysis and generalized differentiation, I: Basic theory","author":"BS Mordukhovich","year":"2006","unstructured":"Mordukhovich, B. S. (2006). Variational analysis and generalized differentiation, I: Basic theory. Berlin: Springer."},{"issue":"1\u20132","key":"2337_CR22","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1007\/s10107-007-0120-x","volume":"116","author":"BS Mordukhovich","year":"2009","unstructured":"Mordukhovich, B. S., Nam, N. M., & Yen, N. D. (2009). Subgradients of marginal functions in parametric mathematical programming. Mathematical Programming, 116(1\u20132), 369\u2013396.","journal-title":"Mathematical Programming"},{"key":"2337_CR23","doi-asserted-by":"crossref","unstructured":"Mordukhovich, B. S., & Nghia, T. T. A. (2013a). Constraint qualifications and optimality conditions for nonconvex semi-infinite and infinite programs. Mathematical Programming, 139, 271\u2013300.","DOI":"10.1007\/s10107-013-0672-x"},{"key":"2337_CR24","doi-asserted-by":"crossref","unstructured":"Mordukhovich, B. S., & Nghia, T. T. A. (2013b). Subdifferentials of nonconvex supremum functions and their applications to semi-infinite and infinite programs with Lipschitzian data. SIAM Journal on Optimization, 23, 406\u2013431.","DOI":"10.1137\/110857738"},{"key":"2337_CR25","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1287\/moor.2013.0622","volume":"39","author":"BS Mordukhovich","year":"2014","unstructured":"Mordukhovich, B. S., & Nghia, T. T. A. (2014). Nonsmooth cone-constrained optimization with applications to semi-infinite programming. Mathematics of Operations Research, 39, 301\u2013324.","journal-title":"Mathematics of Operations Research"},{"issue":"2","key":"2337_CR26","first-page":"155","volume":"1","author":"HV Ngai","year":"2000","unstructured":"Ngai, H. V., Luc, D. T., & Thera, M. (2000). Approximate convex functions. Journal of Nonlinear and Convex Analysis, 1(2), 155\u2013176.","journal-title":"Journal of Nonlinear and Convex Analysis"},{"issue":"11","key":"2337_CR27","doi-asserted-by":"crossref","first-page":"3911","DOI":"10.1016\/j.na.2010.01.008","volume":"72","author":"TI Seidman","year":"2010","unstructured":"Seidman, T. I. (2010). Normal cones to infinite intersections. Nonlinear Analysis, 72(11), 3911\u20133917.","journal-title":"Nonlinear Analysis"},{"key":"2337_CR28","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/s10107-011-0440-8","volume":"134","author":"XY Zheng","year":"2012","unstructured":"Zheng, X. Y., & Ng, K. F. (2012). Subsmooth semi-infinite and infinite optimization problems. Mathematical Programming Series A, 134, 365\u2013393.","journal-title":"Mathematical Programming Series A"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10479-016-2337-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-016-2337-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-016-2337-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,14]],"date-time":"2019-09-14T04:07:31Z","timestamp":1568434051000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10479-016-2337-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,30]]},"references-count":28,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2018,8]]}},"alternative-id":["2337"],"URL":"https:\/\/doi.org\/10.1007\/s10479-016-2337-7","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,9,30]]}}}