{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T13:21:48Z","timestamp":1743081708990,"version":"3.40.3"},"publisher-location":"Cham","reference-count":22,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030218027"},{"type":"electronic","value":"9783030218034"}],"license":[{"start":{"date-parts":[[2019,6,15]],"date-time":"2019-06-15T00:00:00Z","timestamp":1560556800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-21803-4_70","type":"book-chapter","created":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T22:03:24Z","timestamp":1560549804000},"page":"702-710","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["$$\\varPhi -$$ Weak Slater Constraint Qualification in Nonsmooth Multiobjective Semi-infinite Programming"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3147-9531","authenticated-orcid":false,"given":"Ali","family":"Sadeghieh","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7072-1290","authenticated-orcid":false,"given":"David","family":"Barilla","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1953-5198","authenticated-orcid":false,"given":"Giuseppe","family":"Caristi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0397-6415","authenticated-orcid":false,"given":"Nader","family":"Kanzi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,6,15]]},"reference":[{"key":"70_CR1","unstructured":"Antczak, T.: Saddle point criteria and Wolfe duality in nonsmooth \n                    \n                      \n                    \n                    $$(\\Phi ,\\rho )-$$\n                  invex vector optimization problems with inequality and equality constraints. Int. J. Comput. Math. 92(5), 882\u2013907 (2015)"},{"key":"70_CR2","unstructured":"Antczak, T., Stasiak, A.: \n                    \n                      \n                    \n                    $$(\\Phi ,\\rho )-$$\n                  invexity in nonsmooth optimization. Numer. Func. Anal. Optim. 32, 1\u201325 (2015)"},{"key":"70_CR3","doi-asserted-by":"publisher","unstructured":"Caristi, G., Kanzi, M., Soleimani-damaneh, M.: On gap functions for nonsmooth multiobjective optimization problems. Optim. Lett. (2017). \n                    https:\/\/doi.org\/10.1007\/s11590-017-1110-4","DOI":"10.1007\/s11590-017-1110-4"},{"key":"70_CR4","unstructured":"Caristi, G., Ferrara, M., Stefanescu, A.: Semi-infinite multiobjective programming with grneralized invexity. Math. Rep. 62, 217\u2013233 (2010)"},{"key":"70_CR5","doi-asserted-by":"crossref","unstructured":"Caristi, G., Ferrara, M., Stefanescu, A.: Mathematical programming with \n                    \n                      \n                    \n                    $$(\\rho ,\\Phi )$$\n                  -invexity. In: Konnor, I.V., Luc, D.T., Rubinov, A.M. (eds.) Generalized Convexity and Related Topics. Lecture Notes in Economics and Mathematical Systems, vol. 583, pp. 167\u2013176. Springer, Heidelberg (2006)","DOI":"10.1007\/978-3-540-37007-9_9"},{"key":"70_CR6","unstructured":"Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, Interscience (1983)"},{"key":"70_CR7","unstructured":"Ehrgott, M.: Multicriteria Optimization. Springer, Berlin (2005)"},{"key":"70_CR8","doi-asserted-by":"publisher","unstructured":"Goberna, M.A., Kanzi, N.: Optimality conditions in convex multiobjective SIP. Math. Program. (2017). \n                    https:\/\/doi.org\/10.1007\/s10107-016-1081-8","DOI":"10.1007\/s10107-016-1081-8"},{"key":"70_CR9","unstructured":"Goberna, M., Guerra-Vazquez, F., Todorov, M.I.: Constraint qualifications in linear vector semi-infinite optimization. Eur. J. Oper. Res. 227, 32\u201340 (2016)"},{"key":"70_CR10","unstructured":"Goberna, M.A., Guerra-Vazquez, F., Todorov, M.I.: Constraint qualifications in convex vector semi-infinite optimization. Eur. J. Oper. Res. 249, 12\u201321 (2013)"},{"key":"70_CR11","unstructured":"Gopfert, A., Riahi, H., Tammer, C., Zalinescu, C.: Variational Methods in Partial Ordered Spaces. Springer, New York (2003)"},{"key":"70_CR12","unstructured":"Guerraggio, A., Molho, E., Zaffaroni, A.: On the notion of proper efficiency in vector optimization. J. Optim. Theory Appl. 82, 1\u201321 (1994)"},{"key":"70_CR13","unstructured":"Hearn, D.W.: The gap function of a convex program. Oper. Res. Lett. 1, 67\u201371 (1982)"},{"key":"70_CR14","doi-asserted-by":"crossref","unstructured":"Hettich, R., Kortanek, O.: Semi-infinite programming: theory, methods, and applications. SIAM Rev. 35, 380\u2013429 (1993)","DOI":"10.1137\/1035089"},{"key":"70_CR15","unstructured":"Hiriart-Urruty, J.B., Lemarechal, C.: Convex Analysis and Minimization Algorithms. I & II. Springer, Heidelberg (1991)"},{"key":"70_CR16","doi-asserted-by":"publisher","unstructured":"Kanzi, N., Shaker Ardekani, J., Caristi, G.: Optimality scalarization and duality in linear vector semi-infinite programming. Optimization (2018). \n                    https:\/\/doi.org\/10.1080\/02331934.2018.1454921","DOI":"10.1080\/02331934.2018.1454921"},{"key":"70_CR17","doi-asserted-by":"publisher","unstructured":"Kanzi, N.: Necessary and sufficient conditions for (weakly) efficient of nondifferentiable multi-objective semi-infinite programming. Iran. J. Sci. Technol. Trans. A Sci. (2017). \n                    https:\/\/doi.org\/10.1007\/s40995-017-156-6","DOI":"10.1007\/s40995-017-156-6"},{"key":"70_CR18","doi-asserted-by":"crossref","unstructured":"Kanzi, N.: Necessary Optimality conditions for nonsmooth semi-infinite programming problems. J. Global Optim. 49, 713\u2013725 (2011)","DOI":"10.1007\/s10898-010-9561-5"},{"key":"70_CR19","unstructured":"Kanzi, N.: Constraint qualifications in semi-infinite systems and their applications in nonsmooth semi-infinite problems with mixed constraints. SIAM J. Optim. 24, 559\u2013572 (2014)"},{"key":"70_CR20","unstructured":"Kanzi, N.: On strong KKT optimality conditions for multiobjective semi-infinite programming problems with Lipschitzian data. Optim. Lett. 9, 1121\u20131129 (2015)"},{"key":"70_CR21","doi-asserted-by":"publisher","unstructured":"Kanzi, N., Nobakhtian, S.: Optimality conditions for nonsmooth semi-infinite multiobjective programming. Optim. Lett. (2013). \n                    https:\/\/doi.org\/10.1007\/s11590-013-0683-9","DOI":"10.1007\/s11590-013-0683-9"},{"key":"70_CR22","doi-asserted-by":"crossref","unstructured":"L\u00f3pez, M.A., Vercher, E.: Optimality conditions for nondifferentiable convex semi-infinite programming. Math. Program. 27, 307\u2013319 (1983)","DOI":"10.1007\/BF02591906"}],"container-title":["Advances in Intelligent Systems and Computing","Optimization of Complex Systems: Theory, Models, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-21803-4_70","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,11,1]],"date-time":"2019-11-01T05:51:38Z","timestamp":1572587498000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-21803-4_70"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,15]]},"ISBN":["9783030218027","9783030218034"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-21803-4_70","relation":{},"ISSN":["2194-5357","2194-5365"],"issn-type":[{"type":"print","value":"2194-5357"},{"type":"electronic","value":"2194-5365"}],"subject":[],"published":{"date-parts":[[2019,6,15]]},"assertion":[{"value":"15 June 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"WCGO","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"World Congress on Global Optimization","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Metz","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 July 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10 July 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"wcgo2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}