{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T15:30:41Z","timestamp":1759332641520},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2014,2,9]],"date-time":"2014-02-09T00:00:00Z","timestamp":1391904000000},"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":[[2015,2]]},"DOI":"10.1007\/s11590-014-0725-y","type":"journal-article","created":{"date-parts":[[2014,2,8]],"date-time":"2014-02-08T12:17:05Z","timestamp":1391861825000},"page":"245-261","source":"Crossref","is-referenced-by-count":10,"title":["Second-order necessary conditions in locally Lipschitz optimization with inequality constraints"],"prefix":"10.1007","volume":"9","author":[{"given":"Elena","family":"Constantin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,2,9]]},"reference":[{"key":"725_CR1","volume-title":"Set-valued analysis","author":"JP Aubin","year":"1990","unstructured":"Aubin, J.P., Frankowska, H.: Set-valued analysis. Birkh\u00e4user, Boston (1990)"},{"key":"725_CR2","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1137\/0322017","volume":"22","author":"A Auslender","year":"1984","unstructured":"Auslender, A.: Stability in mathematical programming with nondifferentiable data. SIAM J. Control Optim. 22, 239\u2013254 (1984)","journal-title":"SIAM J. Control Optim."},{"issue":"2","key":"725_CR3","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/BF00934107","volume":"31","author":"A Ben-Tal","year":"1980","unstructured":"Ben-Tal, A.: Second-order and related extremality conditions in nonlinear programming. J. Optim. Theory Appl. 31(2), 143\u2013165 (1980)","journal-title":"J. Optim. Theory Appl."},{"key":"725_CR4","volume-title":"Optimization and nonsmooth analysis","author":"FH Clarke","year":"1983","unstructured":"Clarke, F.H.: Optimization and nonsmooth analysis. John Wiley & Sons, New York (1983)"},{"issue":"2","key":"725_CR5","first-page":"42","volume":"10","author":"E Constantin","year":"2006","unstructured":"Constantin, E.: Second-order necessary conditions based on second-order tangent cones. Math. Sci. Res. J. 10(2), 42\u201356 (2006)","journal-title":"Math. Sci. Res. J."},{"issue":"2","key":"725_CR6","first-page":"75","volume":"18","author":"E Constantin","year":"2011","unstructured":"Constantin, E.: Second-order optimality conditions for problems with locally Lipschitz data via tangential directions. Commun. Appl. Nonlinear Anal. 18(2), 75\u201384 (2011)","journal-title":"Commun. Appl. Nonlinear Anal."},{"issue":"2","key":"725_CR7","first-page":"134","volume":"12","author":"E Constantin","year":"2011","unstructured":"Constantin, E., Pavel, N.H.: Optimization and flow invariance via first and second order tangent cones. Afr. Diaspora J. Math. 12(2), 134\u2013148 (2011)","journal-title":"Afr. Diaspora J. Math."},{"key":"725_CR8","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/j.jmaa.2005.01.041","volume":"309","author":"I Ginchev","year":"2005","unstructured":"Ginchev, I., Guerraggio, A., Rocca, M.: Isolated minimizers and proper efficiency for $$C^{0,1}$$ C 0 , 1 constrained vector optimization problems. J. Math. Anal. Appl. 309, 353\u2013368 (2005)","journal-title":"J. Math. Anal. Appl."},{"key":"725_CR9","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.I.: Second-order optimality conditions for problems with $$C^1$$ C 1 data. J. Math. Anal. Appl. 340, 646\u2013657 (2008)","journal-title":"J. Math. Anal. Appl."},{"issue":"1","key":"725_CR10","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/s10492-010-0003-y","volume":"55","author":"I Ginchev","year":"2010","unstructured":"Ginchev, I., Guerraggio, A., Rocca, M.: Locally Lipschitz vector optimization with inequality and equality constraints. Appl. Math. 55(1), 77\u201388 (2010)","journal-title":"Appl. Math."},{"key":"725_CR11","volume-title":"Mathematics of optimization: smooth and nonsmooth case","author":"G Giorgi","year":"2004","unstructured":"Giorgi, G., Guerraggio, A., Thierfelder, J.: Mathematics of optimization: smooth and nonsmooth case. Elsevier, Amsterdam (2004)"},{"key":"725_CR12","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1007\/s11750-008-0058-z","volume":"17","author":"G Giorgi","year":"2009","unstructured":"Giorgi, G., Jimenez, B., Novo, V.: Strong Kuhn\u2013Tucker conditions and constraint qualifications in locally Lipschitz multiobjective optimization problems. Top 17, 288\u2013304 (2009)","journal-title":"Top"},{"key":"725_CR13","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s10957-009-9525-4","volume":"142","author":"C Guti\u00e9rrez","year":"2009","unstructured":"Guti\u00e9rrez, C., Jimenez, B., Nova, V.: New second-order directional derivative and optimality conditions in scalar and vector optimization. J. Optim. Theory Appl. 142, 85\u2013106 (2009)","journal-title":"J. Optim. Theory Appl."},{"key":"725_CR14","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/BF01588951","volume":"14","author":"JB Hiriart-Urruty","year":"1978","unstructured":"Hiriart-Urruty, J.B.: On optimality conditions in nondifferentiable programming. Math. Program. 14, 73\u201386 (1978)","journal-title":"Math. Program."},{"key":"725_CR15","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.jmaa.2009.02.035","volume":"356","author":"VI Ivanov","year":"2009","unstructured":"Ivanov, V.I.: Optimality conditions for an isolated minimum of order two in $$C^1$$ C 1 constrained optimization. J. Math. Anal. Appl. 356, 30\u201341 (2009)","journal-title":"J. Math. Anal. Appl."},{"key":"725_CR16","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1007\/s11590-010-0186-x","volume":"4","author":"VI Ivanov","year":"2010","unstructured":"Ivanov, V.I.: Second-order optimality conditions for inequality constrained problems with locally Lipschitz data. Optim. Lett. 4, 597\u2013608 (2010)","journal-title":"Optim. Lett."},{"key":"725_CR17","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/s11590-010-0250-6","volume":"6","author":"VI Ivanov","year":"2012","unstructured":"Ivanov, V.I.: On the optimality of some classes of invex problems. Optim. Lett. 6, 43\u201354 (2012)","journal-title":"Optim. Lett."},{"key":"725_CR18","unstructured":"Ivanov, V.I.: Duality in nonlinear programming. Optim. Lett. 7(8), 1643\u20131658 (2013)"},{"key":"725_CR19","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s10479-007-0197-x","volume":"157","author":"B Jimenez","year":"2008","unstructured":"Jimenez, B., Novo, V.: Higher-order optimality conditions for strict local minima. Ann. Oper. Res. 157, 183\u2013192 (2008)","journal-title":"Ann. Oper. Res."},{"issue":"1","key":"725_CR20","first-page":"35","volume":"8","author":"PT Kien","year":"2003","unstructured":"Kien, P.T., Luu, D.V.: Higher-order optimality conditions for isolated local minima. Nonlinear Funct. Anal. Appl. 8(1), 35\u201348 (2003)","journal-title":"Nonlinear Funct. Anal. Appl."},{"issue":"3","key":"725_CR21","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1023\/B:JOTA.0000042594.46637.b4","volume":"122","author":"T Maeda","year":"2004","unstructured":"Maeda, T.: Second-order conditions for efficiency in nonsmooth multiobjective problems. J. Optim. Theory Appl. 122(3), 521\u2013538 (2004)","journal-title":"J. Optim. Theory Appl."},{"issue":"5","key":"725_CR22","doi-asserted-by":"crossref","first-page":"1476","DOI":"10.1137\/S0363012992229653","volume":"32","author":"Z P\u00e1les","year":"1994","unstructured":"P\u00e1les, Z., Zeidan, V.M.: Nonsmooth optimum problems with constraints. SIAM J. Control Optim. 32(5), 1476\u20131502 (1994)","journal-title":"SIAM J. Control Optim."},{"key":"725_CR23","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":"725_CR24","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1007\/BF02207780","volume":"80","author":"DE Ward","year":"1994","unstructured":"Ward, D.E.: Characterizations of strict local minima and necessary conditions for weak sharp minima. J. Optim. Theory Appl. 80, 551\u2013571 (1994)","journal-title":"J. Optim. Theory Appl."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-014-0725-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-014-0725-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-014-0725-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T13:11:38Z","timestamp":1559394698000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-014-0725-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2,9]]},"references-count":24,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,2]]}},"alternative-id":["725"],"URL":"https:\/\/doi.org\/10.1007\/s11590-014-0725-y","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,2,9]]}}}