{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:21:14Z","timestamp":1753888874718,"version":"3.41.2"},"reference-count":10,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,5,4]],"date-time":"2006-05-04T00:00:00Z","timestamp":1146700800000},"content-version":"vor","delay-in-days":123,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100007087","name":"University of Isfahan","doi-asserted-by":"publisher","award":["821134"],"award-info":[{"award-number":["821134"]}],"id":[{"id":"10.13039\/501100007087","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>We are concerned with a nonsmooth multiobjective optimization\nproblem with inequality constraints. In order to obtain our main\nresults, we give the definitions of the generalized convex\nfunctions based on the generalized directional derivative. Under\nthe above generalized convexity assumptions, sufficient and\nnecessary conditions for optimality are given without the need of\na constraint qualification. Then we formulate the dual problem\ncorresponding to the primal problem, and some duality results are\nobtained without a constraint qualification.<\/jats:p>","DOI":"10.1155\/ijmms\/2006\/30459","type":"journal-article","created":{"date-parts":[[2006,5,14]],"date-time":"2006-05-14T06:41:30Z","timestamp":1147588890000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Duality without constraint qualification in nonsmooth optimization"],"prefix":"10.1155","volume":"2006","author":[{"given":"S.","family":"Nobakhtian","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,5,4]]},"reference":[{"volume-title":"Nonlinear Programming. Theory and Algorithms","year":"1993","author":"Bazaraa M. S.","key":"e_1_2_1_1_2"},{"key":"e_1_2_1_2_2","series-title":"North-Holland Series in System Science and Engineering","volume-title":"Multiobjective Decision Making. [Theory and Methodology]","author":"Chankong V.","year":"1983"},{"key":"e_1_2_1_3_2","series-title":"Canadian Mathematical Society Series of Monographs and Advanced Texts","volume-title":"Optimization and Nonsmooth Analysis","author":"Clarke F. H.","year":"1983"},{"key":"e_1_2_1_4_2","series-title":"Graduate Texts in Mathematics","volume-title":"Nonsmooth Analysis and Control Theory","author":"Clarke F. H.","year":"1998"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0334270000007219"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1080\/01630568708816246"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022\u2010247X(67)90163\u20101"},{"key":"e_1_2_1_8_2","first-page":"233","article-title":"Duality for generalized convex programming without a constraint qualification","volume":"31","author":"Weir T.","year":"1987","journal-title":"Utilitas Mathematica"},{"key":"e_1_2_1_9_2","first-page":"41","article-title":"Multiple objective programming duality without a constraint qualification","volume":"39","author":"Weir T.","year":"1991","journal-title":"Utilitas Mathematica"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/135625"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2006\/030459.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/IJMMS\/2006\/30459","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,6]],"date-time":"2024-06-06T20:59:23Z","timestamp":1717707563000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/IJMMS\/2006\/30459"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1155\/IJMMS\/2006\/30459"],"URL":"https:\/\/doi.org\/10.1155\/ijmms\/2006\/30459","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2006,1]]},"assertion":[{"value":"2006-05-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"030459"}}