{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,12,27]],"date-time":"2023-12-27T13:54:02Z","timestamp":1703685242460},"reference-count":61,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2015,10,27]],"date-time":"2015-10-27T00:00:00Z","timestamp":1445904000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"CNCS-UEFISCDI, Romania","award":["PN-II-ID-PCE-2011-3-0084"],"award-info":[{"award-number":["PN-II-ID-PCE-2011-3-0084"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2016,3]]},"DOI":"10.1007\/s10957-015-0820-y","type":"journal-article","created":{"date-parts":[[2015,10,27]],"date-time":"2015-10-27T20:13:51Z","timestamp":1445976831000},"page":"802-829","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On Second-Order Generalized Convexity"],"prefix":"10.1007","volume":"168","author":[{"given":"C.","family":"Z\u0103linescu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,10,27]]},"reference":[{"issue":"2\u20133","key":"820_CR1","first-page":"90","volume":"11","author":"B Mond","year":"1974","unstructured":"Mond, B.: Second order duality for nonlinear programs. Opsearch 11(2\u20133), 90\u201399 (1974)","journal-title":"Opsearch"},{"issue":"4","key":"820_CR2","first-page":"283","volume":"28","author":"CR Bector","year":"1986","unstructured":"Bector, C.R., Bector, M.K.: On various duality theorems for second order duality in nonlinear programming. Cahiers Centre \u00c9tudes Rech. Op\u00e9r. 28(4), 283\u2013292 (1986)","journal-title":"Cahiers Centre \u00c9tudes Rech. Op\u00e9r."},{"key":"820_CR3","unstructured":"Bector, C.R., Chandra, S.: (Generalized)-bonvex functions and second order duality in mathematical programming. Technical Report 85-2, Department of Actuarial and Management Sciences, University of Manitoba, Winnipeg, Manitoba, Canada (1985)"},{"issue":"3","key":"820_CR4","first-page":"213","volume":"35","author":"C Z\u0103linescu","year":"1989","unstructured":"Z\u0103linescu, C.: On some types of second order convexity. An. \u015etiin\u0163. Univ. Al. I. Cuza Ia\u015fi Sec\u0163. I a Mat. 35(3), 213\u2013220 (1989)","journal-title":"An. \u015etiin\u0163. Univ. Al. I. Cuza Ia\u015fi Sec\u0163. I a Mat."},{"issue":"3","key":"820_CR5","doi-asserted-by":"crossref","first-page":"815","DOI":"10.1007\/s10957-014-0529-3","volume":"163","author":"C Sommer","year":"2014","unstructured":"Sommer, C.: Geometrical and topological properties of a parameterized binary relation in vector optimization. J. Optim. Theory Appl. 163(3), 815\u2013840 (2014)","journal-title":"J. Optim. Theory Appl."},{"issue":"3","key":"820_CR6","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/BF01593799","volume":"12","author":"DG Mahajan","year":"1977","unstructured":"Mahajan, D.G., Vartak, M.N.: Generalization of some duality theorems in nonlinear programming. Math. Program. 12(3), 293\u2013317 (1977)","journal-title":"Math. Program."},{"issue":"1","key":"820_CR7","first-page":"161","volume":"36","author":"T Antczak","year":"2007","unstructured":"Antczak, T.: Second order convexity and a modified objective function method in mathematical programming. Control Cybern. 36(1), 161\u2013182 (2007)","journal-title":"Control Cybern."},{"issue":"2\u20133","key":"820_CR8","first-page":"183","volume":"1","author":"I Husain","year":"2009","unstructured":"Husain, I., Masoodi, M.: Second order duality in mathematical programming with support functions. J. Inform. Math. Sci. 1(2\u20133), 183\u2013197 (2009)","journal-title":"J. Inform. Math. Sci."},{"key":"820_CR9","volume-title":"Nonlinear Programming","author":"B Martos","year":"1975","unstructured":"Martos, B.: Nonlinear Programming. North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York (1975)"},{"issue":"2\u20133","key":"820_CR10","first-page":"165","volume":"1","author":"I Husain","year":"2009","unstructured":"Husain, I., Ahmed, A., Masoodi, M.: Mixed type second order symmetric duality in multiobjective programming. J. Inform. Math. Sci. 1(2\u20133), 165\u2013182 (2009)","journal-title":"J. Inform. Math. Sci."},{"issue":"4","key":"820_CR11","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/S0893-9659(00)00186-5","volume":"14","author":"I Husain","year":"2001","unstructured":"Husain, I., Rueda, N.G., Jabeen, Z.: Fritz John second-order duality for nonlinear programming. Appl. Math. Lett. 14(4), 513\u2013518 (2001)","journal-title":"Appl. Math. Lett."},{"issue":"2","key":"820_CR12","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.aml.2004.04.008","volume":"18","author":"XM Yang","year":"2005","unstructured":"Yang, X.M., Yang, X.Q., Teo, K.L.: Huard type second-order converse duality for nonlinear programming. Appl. Math. Lett. 18(2), 205\u2013208 (2005)","journal-title":"Appl. Math. Lett."},{"issue":"10","key":"820_CR13","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1016\/j.aml.2006.07.014","volume":"20","author":"TR Gulati","year":"2007","unstructured":"Gulati, T.R., Agarwal, D.: On Huard type second-order converse duality in nonlinear programming. Appl. Math. Lett. 20(10), 1057\u20131063 (2007)","journal-title":"Appl. Math. Lett."},{"issue":"1","key":"820_CR14","first-page":"1","volume":"38","author":"I Ahmad","year":"2014","unstructured":"Ahmad, I., Husain, Z.: Second order fractional symmetric duality. Southeast Asian Bull. Math. 38(1), 1\u201310 (2014)","journal-title":"Southeast Asian Bull. Math."},{"issue":"3","key":"820_CR15","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1016\/S0377-2217(97)00020-9","volume":"104","author":"G Devi","year":"1998","unstructured":"Devi, G.: Symmetric duality for nonlinear programming problem involving $$\\eta $$ \u03b7 -bonvex functions. Eur. J. Oper. Res. 104(3), 615\u2013621 (1998)","journal-title":"Eur. J. Oper. Res."},{"issue":"1\u20132","key":"820_CR16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/01630560701190265","volume":"28","author":"T Antczak","year":"2007","unstructured":"Antczak, T.: A modified objective function method in mathematical programming with second order invexity. Numer. Funct. Anal. Optim. 28(1\u20132), 1\u201312 (2007)","journal-title":"Numer. Funct. Anal. Optim."},{"issue":"5","key":"820_CR17","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/s10492-009-0028-2","volume":"54","author":"T Antczak","year":"2009","unstructured":"Antczak, T.: A second order $$\\eta $$ \u03b7 -approximation method for constrained optimization problems involving second order invex functions. Appl. Math. 54(5), 433\u2013445 (2009)","journal-title":"Appl. Math."},{"issue":"2","key":"820_CR18","first-page":"222","volume":"47","author":"T Antczak","year":"2011","unstructured":"Antczak, T.: Saddle points criteria via a second order $$\\eta $$ \u03b7 -approximation approach for nonlinear mathematical programming involving second order invex functions. Kybernetika (Prague) 47(2), 222\u2013240 (2011)","journal-title":"Kybernetika (Prague)"},{"issue":"1","key":"820_CR19","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1080\/00207160.2011.631529","volume":"89","author":"Q Hu","year":"2012","unstructured":"Hu, Q., Chen, Y., Jian, J.: Second-order duality for non-differentiable minimax fractional programming. Int. J. Comput. Math. 89(1), 11\u201316 (2012)","journal-title":"Int. J. Comput. Math."},{"issue":"6","key":"820_CR20","doi-asserted-by":"crossref","first-page":"3509","DOI":"10.1016\/j.nonrwa.2011.06.011","volume":"12","author":"Q Hu","year":"2011","unstructured":"Hu, Q., Yang, G., Jian, J.: On second order duality for minimax fractional programming. Nonlinear Anal. Real World Appl. 12(6), 3509\u20133514 (2011)","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"820_CR21","first-page":"143","volume":"24","author":"CR Bector","year":"1987","unstructured":"Bector, C.R., Chandra, S.: Generalized bonvexity and higher order duality for fractional programming. Opsearch 24, 143\u2013154 (1987)","journal-title":"Opsearch"},{"issue":"2","key":"820_CR22","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1007\/s11590-008-0107-4","volume":"3","author":"Z Husain","year":"2009","unstructured":"Husain, Z., Ahmad, I., Sharma, S.: Second order duality for minmax fractional programming. Optim. Lett. 3(2), 277\u2013286 (2009)","journal-title":"Optim. Lett."},{"issue":"11","key":"820_CR23","doi-asserted-by":"crossref","first-page":"1265","DOI":"10.1080\/01630563.2013.763348","volume":"34","author":"GJ Zalmai","year":"2013","unstructured":"Zalmai, G.J.: Second-order parameter-free duality models in semi-infinite minmax fractional programming. Numer. Funct. Anal. Optim. 34(11), 1265\u20131298 (2013)","journal-title":"Numer. Funct. Anal. Optim."},{"issue":"4","key":"820_CR24","doi-asserted-by":"crossref","first-page":"727","DOI":"10.4134\/JKMS.2013.50.4.727","volume":"50","author":"GJ Zalmai","year":"2013","unstructured":"Zalmai, G.J.: Second-order univex functions and generalized duality models for multiobjective programming problems containing arbitrary norms. J. Korean Math. Soc. 50(4), 727\u2013753 (2013)","journal-title":"J. Korean Math. Soc."},{"key":"820_CR25","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1016\/j.cam.2013.06.044","volume":"255","author":"SK Gupta","year":"2014","unstructured":"Gupta, S.K., Dangar, D.: On second-order duality for nondifferentiable minimax fractional programming. J. Comput. Appl. Math. 255, 878\u2013886 (2014)","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"820_CR26","first-page":"36","volume":"28","author":"S Pandey","year":"1991","unstructured":"Pandey, S.: Duality for multiobjective fractional programming involving generalized $$\\eta $$ \u03b7 -bonvex functions. Opsearch 28(1), 36\u201343 (1991)","journal-title":"Opsearch"},{"issue":"3","key":"820_CR27","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1016\/S0377-2217(02)00154-6","volume":"144","author":"SK Suneja","year":"2003","unstructured":"Suneja, S.K., Lalitha, C.S., Khurana, S.: Second order symmetric duality in multiobjective programming. Eur. J. Oper. Res. 144(3), 492\u2013500 (2003)","journal-title":"Eur. J. Oper. Res."},{"issue":"5","key":"820_CR28","first-page":"665","volume":"35","author":"I Ahmad","year":"2004","unstructured":"Ahmad, I., Husain, Z.: On nondifferentiable second order symmetric duality in mathematical programming. Indian J. Pure Appl. Math. 35(5), 665\u2013676 (2004)","journal-title":"Indian J. Pure Appl. Math."},{"issue":"3","key":"820_CR29","doi-asserted-by":"crossref","first-page":"402","DOI":"10.1016\/j.ejor.2009.08.019","volume":"204","author":"I Ahmad","year":"2010","unstructured":"Ahmad, I., Husain, Z.: On multiobjective second order symmetric duality with cone constraints. Eur. J. Oper. Res. 204(3), 402\u2013409 (2010)","journal-title":"Eur. J. Oper. Res."},{"issue":"1\u20133","key":"820_CR30","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.ins.2004.06.002","volume":"173","author":"I Ahmad","year":"2005","unstructured":"Ahmad, I.: Second order symmetric duality in nondifferentiable multiobjective programming. Inform. Sci. 173(1\u20133), 23\u201334 (2005)","journal-title":"Inform. Sci."},{"issue":"1","key":"820_CR31","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.jmaa.2005.02.004","volume":"310","author":"TR Gulati","year":"2005","unstructured":"Gulati, T.R., Gupta, S.K.: Wolfe type second-order symmetric duality in nondifferentiable programming. J. Math. Anal. Appl. 310(1), 247\u2013253 (2005)","journal-title":"J. Math. Anal. Appl."},{"issue":"3","key":"820_CR32","first-page":"181","volume":"4","author":"TR Gulati","year":"2007","unstructured":"Gulati, T.R., Gupta, S.K.: Second-order symmetric duality for minimax mixed integer programs over cones. Int. J. Oper. Res. (Taichung) 4(3), 181\u2013188 (2007)","journal-title":"Int. J. Oper. Res. (Taichung)"},{"issue":"1\u20132","key":"820_CR33","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.cam.2007.08.021","volume":"220","author":"TR Gulati","year":"2008","unstructured":"Gulati, T.R., Gupta, S.K., Ahmad, I.: Second-order symmetric duality with cone constraints. J. Comput. Appl. Math. 220(1\u20132), 347\u2013354 (2008)","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"820_CR34","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.ejor.2009.12.024","volume":"205","author":"TR Gulati","year":"2010","unstructured":"Gulati, T.R., Saini, H., Gupta, S.K.: Second-order multiobjective symmetric duality with cone constraints. Eur. J. Oper. Res. 205(2), 247\u2013252 (2010)","journal-title":"Eur. J. Oper. Res."},{"issue":"2","key":"820_CR35","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1007\/s11590-009-0161-6","volume":"4","author":"TR Gulati","year":"2010","unstructured":"Gulati, T.R., Mehndiratta, G.: Nondifferentiable multiobjective Mond\u2013Weir type second-order symmetric duality over cones. Optim. Lett. 4(2), 293\u2013309 (2010)","journal-title":"Optim. Lett."},{"issue":"6","key":"820_CR36","doi-asserted-by":"crossref","first-page":"3373","DOI":"10.1016\/j.nonrwa.2011.06.001","volume":"12","author":"N Kailey","year":"2011","unstructured":"Kailey, N., Gupta, S.K., Dangar, D.: Mixed second-order multiobjective symmetric duality with cone constraints. Nonlinear Anal. Real World Appl. 12(6), 3373\u20133383 (2011)","journal-title":"Nonlinear Anal. Real World Appl."},{"issue":"2","key":"820_CR37","first-page":"283","volume":"14","author":"Q Hu","year":"2012","unstructured":"Hu, Q., Yang, G., Chen, Y., Jian, J.: Mixed type second-order symmetric duality for nonlinear programming problems involving $$\\eta $$ \u03b7 -bonvex functions. J. Comput. Anal. Appl. 14(2), 283\u2013289 (2012)","journal-title":"J. Comput. Anal. Appl."},{"issue":"3","key":"820_CR38","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/s10957-006-9113-9","volume":"130","author":"SK Mishra","year":"2006","unstructured":"Mishra, S.K., Rueda, N.G.: Second-order duality for nondifferentiable minimax programming involving generalized type I functions. J. Optim. Theory Appl. 130(3), 477\u2013486 (2006)","journal-title":"J. Optim. Theory Appl."},{"key":"820_CR39","doi-asserted-by":"crossref","unstructured":"Padhan, S.K., Nahak, C.: Second-order symmetric duality with generalized invexity. In: Topics in Nonconvex Optimization, Springer Optimization and Its Applications, vol. 50, pp. 205\u2013214. Springer, New York (2011)","DOI":"10.1007\/978-1-4419-9640-4_12"},{"issue":"3","key":"820_CR40","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1016\/S0377-2217(99)00339-2","volume":"126","author":"SK Mishra","year":"2000","unstructured":"Mishra, S.K.: Multiobjective second order symmetric duality with cone constraints. European J. Oper. Res. 126(3), 675\u2013682 (2000)","journal-title":"European J. Oper. Res."},{"key":"820_CR41","unstructured":"Egudo, R.R., Hanson, M.A.: Second order duality in multiobjective programming. Technical Report M-886, Department of Statistics, Florida State University, Tallahassee, Florida, 32306\u20133033. www.stat.fsu.edu\/techreports\/scannedinreports\/M886 (1993)"},{"issue":"2","key":"820_CR42","first-page":"267","volume":"3","author":"B Aghezzaf","year":"2009","unstructured":"Aghezzaf, B., Naimi, M.: Duality for multiobjective programming involving generalized second order $$V$$ V -invexity. J. Math. Sci. Adv. Appl. 3(2), 267\u2013278 (2009)","journal-title":"J. Math. Sci. Adv. Appl."},{"key":"820_CR43","first-page":"1","volume":"187","author":"SK Gupta","year":"2012","unstructured":"Gupta, S.K., Dangar, D., Kumar, S.: Second-order duality for a nondifferentiable minimax fractional programming under generalized $$\\alpha $$ \u03b1 -univexity. J. Inequal. Appl. 187, 1\u201311 (2012)","journal-title":"J. Inequal. Appl."},{"issue":"5","key":"820_CR44","first-page":"699","volume":"35","author":"XM Yang","year":"2004","unstructured":"Yang, X.M., Yang, X.Q., Teo, K.L., Hou, S.H.: Second-order duality for nonlinear programming. Indian J. Pure Appl. Math. 35(5), 699\u2013708 (2004)","journal-title":"Indian J. Pure Appl. Math."},{"issue":"3","key":"820_CR45","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1016\/S0377-2217(02)00156-X","volume":"144","author":"XM Yang","year":"2003","unstructured":"Yang, X.M., Yang, X.Q., Teo, K.L.: Non-differentiable second order symmetric duality in mathematical programming with $$F$$ F -convexity. Eur. J. Oper. Res. 144(3), 554\u2013559 (2003)","journal-title":"Eur. J. Oper. Res."},{"issue":"2","key":"820_CR46","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1016\/j.ejor.2003.04.007","volume":"164","author":"XM Yang","year":"2005","unstructured":"Yang, X.M., Yang, X.Q., Teo, K.L., Hou, S.H.: Second order symmetric duality in non-differentiable multiobjective programming with $$F$$ F -convexity. Eur. J. Oper. Res. 164(2), 406\u2013416 (2005)","journal-title":"Eur. J. Oper. Res."},{"issue":"7\u20138","key":"820_CR47","first-page":"725","volume":"25","author":"M Hachimi","year":"2004","unstructured":"Hachimi, M., Aghezzaf, B.: Second order duality in multiobjective programming involving generalized type I functions. Numer. Funct. Anal. Optim. 25(7\u20138), 725\u2013736 (2004)","journal-title":"Numer. Funct. Anal. Optim."},{"issue":"1","key":"820_CR48","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.cam.2007.03.022","volume":"215","author":"I Ahmad","year":"2008","unstructured":"Ahmad, I., Husain, Z., Sharma, S.: Second-order duality in nondifferentiable minmax programming involving type-I functions. J. Comput. Appl. Math. 215(1), 91\u2013102 (2008)","journal-title":"J. Comput. Appl. Math."},{"issue":"7","key":"820_CR49","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1016\/j.aml.2004.05.010","volume":"18","author":"I Ahmad","year":"2005","unstructured":"Ahmad, I., Husain, Z.: Nondifferentiable second order symmetric duality in multiobjective programming. Appl. Math. Lett. 18(7), 721\u2013728 (2005)","journal-title":"Appl. Math. Lett."},{"issue":"2","key":"820_CR50","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1016\/j.nonrwa.2010.09.004","volume":"12","author":"I Ahmad","year":"2011","unstructured":"Ahmad, I., Husain, Z., Al-Homidan, S.: Second-order duality in nondifferentiable fractional programming. Nonlinear Anal. Real World Appl. 12(2), 1103\u20131110 (2011)","journal-title":"Nonlinear Anal. Real World Appl."},{"issue":"20","key":"820_CR51","doi-asserted-by":"crossref","first-page":"3094","DOI":"10.1016\/j.ins.2005.08.003","volume":"176","author":"I Ahmad","year":"2006","unstructured":"Ahmad, I., Husain, Z.: Second order $$(F,\\alpha,\\rho, d)$$ ( F , \u03b1 , \u03c1 , d ) -convexity and duality in multiobjective programming. Inform. Sci. 176(20), 3094\u20133103 (2006)","journal-title":"Inform. Sci."},{"issue":"16","key":"820_CR52","doi-asserted-by":"crossref","first-page":"3532","DOI":"10.1016\/j.ins.2011.03.022","volume":"181","author":"I Ahmad","year":"2011","unstructured":"Ahmad, I., Husain, Z.: Erratum to \u201cSecond order $$(F, \\alpha, \\rho, d)$$ ( F , \u03b1 , \u03c1 , d ) -convexity and duality in multiobjective programming\u201d [Inform. Sci. 176 (2006) 3094\u20133103] [MR2247618]. Inform. Sci. 181(16), 3532 (2011)","journal-title":"Inform. Sci."},{"issue":"1","key":"820_CR53","doi-asserted-by":"crossref","first-page":"135","DOI":"10.2298\/FIL1301135A","volume":"27","author":"I Ahmad","year":"2013","unstructured":"Ahmad, I.: Second order nondifferentiable minimax fractional programming with square root terms. Filomat 27(1), 135\u2013142 (2013)","journal-title":"Filomat"},{"key":"820_CR54","doi-asserted-by":"crossref","unstructured":"Gupta, S.K., Dangar, D.: Second-order duality for nondifferentiable minimax fractional programming involving ( $${F},\\rho $$ F , \u03c1 )-convexity. In: Proceedings of the International Multi Conference of Engineers and Computer Scientists, vol. II, Hong Kong, pp. 1501\u20131506. (2012)","DOI":"10.1186\/1029-242X-2012-306"},{"issue":"1","key":"820_CR55","doi-asserted-by":"crossref","first-page":"1","DOI":"10.11121\/ijocta.01.2013.00122","volume":"3","author":"TR Gulati","year":"2013","unstructured":"Gulati, T.R., Verma, K.: Mixed type second-order symmetric duality under $$F$$ F -convexity. Int. J. Optim. Control, Theor. Appl. (IJOCTA) 3(1), 1\u20135 (2013)","journal-title":"Int. J. Optim. Control, Theor. Appl. (IJOCTA)"},{"issue":"14","key":"820_CR56","doi-asserted-by":"crossref","first-page":"7602","DOI":"10.1016\/j.amc.2012.01.027","volume":"218","author":"S Gupta","year":"2012","unstructured":"Gupta, S., Kailey, N.: Multiobjective second-order mixed symmetric duality with a square root term. Appl. Math. Comput. 218(14), 7602\u20137613 (2012)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"820_CR57","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/S0022-247X(03)00359-7","volume":"285","author":"B Aghezzaf","year":"2003","unstructured":"Aghezzaf, B.: Second order mixed type duality in multiobjective programming problems. J. Math. Anal. Appl. 285(1), 97\u2013106 (2003)","journal-title":"J. Math. Anal. Appl."},{"issue":"11\u201312","key":"820_CR58","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1080\/01630560701749664","volume":"28","author":"TR Gulati","year":"2007","unstructured":"Gulati, T.R., Agarwal, D.: Second-order duality in multiobjective programming involving $$(F,\\alpha,\\rho, d)$$ ( F , \u03b1 , \u03c1 , d ) - $$V$$ V -type I functions. Numer. Funct. Anal. Optim. 28(11\u201312), 1263\u20131277 (2007)","journal-title":"Numer. Funct. Anal. Optim."},{"issue":"5\u20138","key":"820_CR59","first-page":"303","volume":"4","author":"P Pandian","year":"2010","unstructured":"Pandian, P., Natarajan, G.: Second order $$(b, F)$$ ( b , F ) -convexity in multiobjective nonlinear programming. Int. J. Math. Anal. (Ruse) 4(5\u20138), 303\u2013314 (2010)","journal-title":"Int. J. Math. Anal. (Ruse)"},{"key":"820_CR60","first-page":"135","volume":"13","author":"P Pandian","year":"2009","unstructured":"Pandian, P., Natarajan, G.: Multiobjective nonlinear programming problems involving second order $$(b, F)$$ ( b , F ) -type I functions. J. Phys. Sci. 13, 135\u2013147 (2009)","journal-title":"J. Phys. Sci."},{"key":"820_CR61","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1016\/j.amc.2013.10.050","volume":"227","author":"T Antczak","year":"2014","unstructured":"Antczak, T., Zalmai, G.J.: Second order $$(\\varPhi ,\\rho )\\text{- }V$$ ( \u03a6 , \u03c1 ) - V -invexity and duality for semi-infinite minimax fractional programming. Appl. Math. Comput. 227, 831\u2013856 (2014)","journal-title":"Appl. Math. Comput."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-015-0820-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-015-0820-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-015-0820-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,1]],"date-time":"2019-09-01T01:24:45Z","timestamp":1567301085000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-015-0820-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,27]]},"references-count":61,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,3]]}},"alternative-id":["820"],"URL":"https:\/\/doi.org\/10.1007\/s10957-015-0820-y","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10,27]]}}}