{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:15:18Z","timestamp":1762323318048},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2009,11,4]],"date-time":"2009-11-04T00:00:00Z","timestamp":1257292800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2010,5]]},"DOI":"10.1007\/s10107-009-0318-1","type":"journal-article","created":{"date-parts":[[2009,11,3]],"date-time":"2009-11-03T13:03:10Z","timestamp":1257253390000},"page":"199-223","source":"Crossref","is-referenced-by-count":44,"title":["On second-order Fritz John type optimality conditions in nonsmooth multiobjective programming"],"prefix":"10.1007","volume":"123","author":[{"given":"C.","family":"Guti\u00e9rrez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"Jim\u00e9nez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V.","family":"Novo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,11,4]]},"reference":[{"key":"318_CR1","volume-title":"Set-valued analysis","author":"J.P. Aubin","year":"1990","unstructured":"Aubin J.P., Frankowska H.: Set-valued analysis. Birkha\u00fcser, Boston (1990)"},{"key":"318_CR2","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/s10107-007-0094-8","volume":"113","author":"D. Bedna\u0159\u00edk","year":"2008","unstructured":"Bedna\u0159\u00edk D., Pastor K.: On second-order conditions in unconstrained optimization. Math. Program. 113, 283\u2013298 (2008)","journal-title":"Math. Program."},{"key":"318_CR3","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/BFb0120982","volume":"19","author":"A. Ben-Tal","year":"1982","unstructured":"Ben-Tal A., Zowe J.: A unified theory of first and second order conditions for extremum problems in topological vector spaces. Math. Program. Stud. 19, 39\u201376 (1982)","journal-title":"Math. Program. Stud."},{"key":"318_CR4","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1007\/BF01585095","volume":"24","author":"A. Ben-Tal","year":"1982","unstructured":"Ben-Tal A., Zowe J.: Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems. Math. Program. 24, 70\u201391 (1982)","journal-title":"Math. Program."},{"key":"318_CR5","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1007\/BF00942193","volume":"47","author":"A. Ben-Tal","year":"1985","unstructured":"Ben-Tal A., Zowe J.: Directional derivatives in nonsmooth optimization. J. Optim. Theory Appl. 47, 483\u2013490 (1985)","journal-title":"J. Optim. Theory Appl."},{"key":"318_CR6","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1137\/S1052623496306760","volume":"9","author":"J.F. Bonnans","year":"1999","unstructured":"Bonnans 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":"318_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1394-9","volume-title":"Perturbation analysis of optimization problems","author":"J.F. Bonnans","year":"2000","unstructured":"Bonnans J.F., Shapiro A.: Perturbation analysis of optimization problems. Springer-Verlag, New York (2000)"},{"key":"318_CR8","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1080\/02331939608844224","volume":"37","author":"M. Castellani","year":"1996","unstructured":"Castellani M., Pappalardo M.: Local second-order approximations and applications in optimization. Optimization 37, 305\u2013321 (1996)","journal-title":"Optimization"},{"key":"318_CR9","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":"318_CR10","unstructured":"Dubovitskii, A.Y., Milyutin, A.A.: Extremum problems in the presence of restrictions. U.S.S.R. Comput. Math. Math. Phys. 5, 1\u201380 (1965), translation from Zh. Vychisl. Mat. Mat. Fiz. 5, 395\u2013453 (1965)"},{"key":"318_CR11","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/BF00425960","volume":"4","author":"P.G. Georgiev","year":"1996","unstructured":"Georgiev P.G., Zlateva N.P.: Second order subdifferentials of C 1,1 functions and optimality conditions. Set-Valued Anal. 4, 101\u2013117 (1996)","journal-title":"Set-Valued Anal."},{"key":"318_CR12","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1137\/040612713","volume":"45","author":"H. Gfrerer","year":"2006","unstructured":"Gfrerer H.: Second-Order optimality conditions for scalar and vector optimization problems in Banach spaces. SIAM J. Control Optim. 45, 972\u2013997 (2006)","journal-title":"SIAM J. Control Optim."},{"issue":"2\u20133","key":"318_CR13","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s10107-005-0621-4","volume":"104","author":"I. Ginchev","year":"2005","unstructured":"Ginchev I., Guerraggio A., Rocca M.: Second-order conditions in C 1,1 constrained vector optimization. Math. Program. 104(2\u20133), 389\u2013405 (2005)","journal-title":"Math. Program."},{"key":"318_CR14","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10492-006-0002-1","volume":"51","author":"I. Ginchev","year":"2006","unstructured":"Ginchev I., Guerraggio A., Rocca M.: From scalar to vector optimization. Appl. Math. 51, 5\u201336 (2006)","journal-title":"Appl. Math."},{"key":"318_CR15","doi-asserted-by":"crossref","unstructured":"Ginchev, I., Guerraggio, A., Rocca, M.: Second-order conditions in C 1,1 vector optimization with inequality and equality constraints. In: Seeger, A. (ed.) Recent Advances in Optimization, Lecture Notes in Econom. and Math. Systems 563, pp. 29\u201344. Springer-Verlag, Berlin (2006)","DOI":"10.1007\/3-540-28258-0_3"},{"key":"318_CR16","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1016\/j.jmaa.2007.08.053","volume":"340","author":"I. Ginchev","year":"2008","unstructured":"Ginchev I., Ivanov V.: Second-order optimality conditions for problems with C 1 data. J. Math. Anal. Appl. 340, 646\u2013657 (2008)","journal-title":"J. Math. Anal. Appl."},{"key":"318_CR17","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1023\/A:1017519922669","volume":"109","author":"A. Guerraggio","year":"2001","unstructured":"Guerraggio A., Luc D.T.: Optimality conditions for C 1,1 vector optimization problems. J. Optim. Theory Appl. 109, 615\u2013629 (2001)","journal-title":"J. Optim. Theory Appl."},{"key":"318_CR18","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1023\/A:1022114319999","volume":"116","author":"A. Guerraggio","year":"2003","unstructured":"Guerraggio A., Luc D.T.: Optimality conditions for C 1,1 constrained multiobjective problems. J. Optim. Theory Appl. 116, 117\u2013129 (2003)","journal-title":"J. Optim. Theory Appl."},{"key":"318_CR19","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/BF01442169","volume":"11","author":"J.B. Hiriart-Urruty","year":"1984","unstructured":"Hiriart-Urruty J.B., Strodiot J.J., Nguyen V.H.: Generalized hessian matrix and second-order optimality conditions for problems with C 1,1 data. Appl. Math. Optim. 11, 43\u201354 (1984)","journal-title":"Appl. Math. Optim."},{"key":"318_CR20","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":"318_CR21","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":"318_CR22","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1016\/S0022-247X(03)00337-8","volume":"284","author":"B. Jim\u00e9nez","year":"2003","unstructured":"Jim\u00e9nez B., Novo V.: First and second order sufficient conditions for strict minimality in nonsmooth vector optimization. J. Math. Anal. Appl. 284, 496\u2013510 (2003)","journal-title":"J. Math. Anal. Appl."},{"key":"318_CR23","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s001860300283","volume":"58","author":"B. Jim\u00e9nez","year":"2003","unstructured":"Jim\u00e9nez B., Novo V.: Second order necessary conditions in set constrained differentiable vector optimization. Math. Methods Oper. Res. 58, 299\u2013317 (2003)","journal-title":"Math. Methods Oper. Res."},{"key":"318_CR24","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":"318_CR25","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":"318_CR26","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/s10957-007-9169-1","volume":"133","author":"P.Q. 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":"318_CR27","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1080\/02331938808843333","volume":"19","author":"D. Klatte","year":"1988","unstructured":"Klatte D., Tammer D.: On second-order sufficient optimality conditions for C 1,1 optimizations problems. Optimization 19, 169\u2013179 (1988)","journal-title":"Optimization"},{"key":"318_CR28","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1023\/A:1023068513188","volume":"42","author":"L. Liu","year":"1997","unstructured":"Liu L., K\u0159\u00ed\u017eek M.: The second order optimality conditions for nonlinear mathematical programming with C 1,1 data. Appl. Math. 42, 311\u2013320 (1997)","journal-title":"Appl. Math."},{"key":"318_CR29","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1023\/A:1022272728208","volume":"45","author":"L. Liu","year":"2000","unstructured":"Liu L., Neittaanm\u00e4ki P., K\u0159\u00ed\u017eek M.: Second-order optimality conditions for nondominated solutions of multiobjective programming with C 1,1 data. Appl. Math. 45, 381\u2013397 (2000)","journal-title":"Appl. Math."},{"key":"318_CR30","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1287\/moor.15.3.467","volume":"15","author":"Y. Maruyama","year":"1990","unstructured":"Maruyama Y.: Second-order necessary conditions for nonlinear optimization problems in Banach spaces and their application to an optimal control problem. Math. Oper. Res. 15, 467\u2013482 (1990)","journal-title":"Math. Oper. Res."},{"key":"318_CR31","first-page":"509","volume":"40","author":"Y. Maruyama","year":"1994","unstructured":"Maruyama Y.: Second-order necessary conditions for nonlinear optimization problems in Banach spaces by the use of Neustadt derivative. Math. Japon. 40, 509\u2013522 (1994)","journal-title":"Math. Japon."},{"key":"318_CR32","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/BF01582222","volume":"67","author":"J.P. Penot","year":"1994","unstructured":"Penot J.P.: Optimality conditions in mathematical programming and composite optimization. Math. Program. 67, 225\u2013245 (1994)","journal-title":"Math. Program."},{"key":"318_CR33","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1137\/S0363012996311095","volume":"37","author":"J.P. 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":"318_CR34","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-02431-3","volume-title":"Variational analysis","author":"R.T. Rockafellar","year":"1998","unstructured":"Rockafellar R.T., Wets R.J.: Variational analysis. Springer, Berlin (1998)"},{"key":"318_CR35","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/BF01027635","volume":"1","author":"D.E. Ward","year":"1993","unstructured":"Ward D.E.: Calculus for parabolic second-order derivatives. Set Valued Anal. 1, 213\u2013246 (1993)","journal-title":"Set Valued Anal."}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-009-0318-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-009-0318-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-009-0318-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T09:50:07Z","timestamp":1559123407000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-009-0318-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11,4]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,5]]}},"alternative-id":["318"],"URL":"https:\/\/doi.org\/10.1007\/s10107-009-0318-1","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11,4]]}}}