{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T19:51:32Z","timestamp":1779911492119,"version":"3.53.1"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2011,10,5]],"date-time":"2011-10-05T00:00:00Z","timestamp":1317772800000},"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":[[2013,1]]},"DOI":"10.1007\/s11590-011-0402-3","type":"journal-article","created":{"date-parts":[[2011,10,4]],"date-time":"2011-10-04T11:43:47Z","timestamp":1317728627000},"page":"127-135","source":"Crossref","is-referenced-by-count":25,"title":["Optimality via generalized approximate convexity and quasiefficiency"],"prefix":"10.1007","volume":"7","author":[{"given":"Davinder","family":"Bhatia","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anjana","family":"Gupta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pooja","family":"Arora","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2011,10,5]]},"reference":[{"key":"402_CR1","volume-title":"Principles of Optimization Theory","author":"C.R. Bector","year":"2005","unstructured":"Bector C.R., Chandra S., Dutta J.: Principles of Optimization Theory. Narosa Publishing House, India (2005)"},{"key":"402_CR2","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1080\/02331939408844012","volume":"31","author":"D. Bhatia","year":"1994","unstructured":"Bhatia D., Jain P.: Generalized (F, \u03c1) convexity and duality for nonsmooth multiobjective programs. Optimization. 31, 153\u2013164 (1994)","journal-title":"Optimization."},{"issue":"1","key":"402_CR3","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s10479-007-0186-0","volume":"154","author":"A. Chinchuluun","year":"2007","unstructured":"Chinchuluun A., Pardalos P.M.: A survey of recent developments in multiobjective optimization. Ann. Oper. Res. 154(1), 29\u201350 (2007)","journal-title":"Ann. Oper. Res."},{"key":"402_CR4","volume-title":"Pareto Optimality, Game Theory and Equilibria","year":"2008","unstructured":"Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L. (eds): Pareto Optimality, Game Theory and Equilibria. Springer, Berlin (2008)"},{"key":"402_CR5","volume-title":"Optimization and Nonsmooth Analysis","author":"F.H. Clarke","year":"1983","unstructured":"Clarke F.H.: Optimization and Nonsmooth Analysis. Willey-Inteerscience, New York (1983)"},{"key":"402_CR6","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1081\/NFA-100108312","volume":"22","author":"J. Dutta","year":"2001","unstructured":"Dutta J., Vetrivel V.: On approximate minima in vector optimization. Numer. Funct. Anal. Optim. 22, 845\u2013859 (2001)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"402_CR7","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/0022-247X(89)90321-1","volume":"138","author":"R. Egudo","year":"1989","unstructured":"Egudo R.: Efficiency and generalized convex duality for multi-objective programs. J. Math. Anal. Appl. 138, 84\u201394 (1989)","journal-title":"J. Math. Anal. Appl."},{"key":"402_CR8","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/S0377-2217(03)00206-6","volume":"157","author":"M.G. Govil","year":"2004","unstructured":"Govil M.G., Mehra A.: $${\\varepsilon}$$ -optimality for multiobjective programming on a Banach space. Eur. J. Oper. Res. 157, 106\u2013112 (2004)","journal-title":"Eur. J. Oper. Res."},{"key":"402_CR9","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1017\/S0004972700035656","volume":"74","author":"A. Gupta","year":"2006","unstructured":"Gupta A., Mehra A., Bhatia D.: Approximate convexity in vector optimization. Bull. Aust. Math. Soc. 74, 207\u2013218 (2006)","journal-title":"Bull. Aust. Math. Soc."},{"key":"402_CR10","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/BF02591683","volume":"37","author":"M.A. Hanson","year":"1987","unstructured":"Hanson M.A., Mond B.: Necessary and sufficient conditions in constrained optimization. Math. Program. 37, 51\u201358 (1987)","journal-title":"Math. Program."},{"key":"402_CR11","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1017\/S0334270000007372","volume":"34","author":"V. Jeykumar","year":"1992","unstructured":"Jeykumar V., Mond B.: On generalized convex mathematical programming. J. Aust. Math. Soc. Ser. B. 34, 43\u201353 (1992)","journal-title":"J. Aust. Math. Soc. Ser. B."},{"issue":"4","key":"402_CR12","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1023\/A:1026041403408","volume":"27","author":"Z.-A. Liang","year":"2003","unstructured":"Liang Z.-A., Huang H.X., Pardalos P.M.: Efficiency conditions and duality for a class of multiobjective fractional programming problem. J. Glob. Optim. 27(4), 447\u2013471 (2003)","journal-title":"J. Glob. Optim."},{"key":"402_CR13","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/BF00940466","volume":"69","author":"J.C. Liu","year":"1991","unstructured":"Liu J.C.: $${\\varepsilon}$$ -duality theorem of nondifferentiable nonconvex multiobjective programming. J. Optim. Theory Appl. 69, 153\u2013167 (1991)","journal-title":"J. Optim. Theory Appl."},{"key":"402_CR14","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/BF00936165","volume":"43","author":"P. Loridan","year":"1984","unstructured":"Loridan P.: $${\\varepsilon}$$ -solutions in vector minimization problems. J. Optim. Theory Appl. 43, 265\u2013276 (1984)","journal-title":"J. Optim. Theory Appl."},{"key":"402_CR15","first-page":"155","volume":"1","author":"H.V. Ngai","year":"2000","unstructured":"Ngai H.V., Luc D., Thera M.: Approximate convex functions. J. Nonlinear Convex Anal. 1, 155\u2013176 (2000)","journal-title":"J. Nonlinear Convex Anal."},{"key":"402_CR16","first-page":"73","volume-title":"Generalized Convexity and Related Topics","author":"P.M. Pardalos","year":"2007","unstructured":"Pardalos P.M., Yuan D., Liu X., Chinchuluun A.: Optimality conditions and duality for multiobjective programming involving (c, \u03b1, \u03c1, d)type-I functions. In: Konnov, I.V., Luc, D.T., Rubinov, A.M. (eds) Generalized Convexity and Related Topics, pp. 73\u201387. Springer, Berlin (2007)"}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-011-0402-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11590-011-0402-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-011-0402-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T17:11:30Z","timestamp":1559409090000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11590-011-0402-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,5]]},"references-count":16,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,1]]}},"alternative-id":["402"],"URL":"https:\/\/doi.org\/10.1007\/s11590-011-0402-3","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"value":"1862-4472","type":"print"},{"value":"1862-4480","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,10,5]]}}}