Second-order duality for a nondifferentiable minimax fractional programming under generalized α-univexity
In this paper, we concentrate our study to derive appropriate duality theorems for two types of second-order dual models of a nondifferentiable minimax fractional programming problem involving second-order α-univex functions. Examples to show the existence of α-univex functions have also been illustrated. Several known results including many recent works are obtained as special cases.
MSC: 49J35, 90C32, 49N15.
- Schmitendorf WE: Necessary conditions and sufficient conditions for static minmax problems. J. Math. Anal. Appl. 1977, 57:683–693. CrossRef
- Ahmad I: Optimality conditions and duality in fractional minimax programming involving generalized ρ -invexity. Int. J. Manag. Syst. 2003, 19:165–180.
- Ahmad I: On second-order duality for minimax fractional programming problems with generalized convexity. Abstr. Appl. Anal. 2011. doi:10.1155/2011/563924
- Ahmad I, Gupta SK, Kailey N, Agarwal RP:Duality in nondifferentiable minimax fractional programming with -invexity. J. Inequal. Appl. 2011. doi:10.1186/1029–242X-2011–75
- Ahmad I, Husain Z: Duality in nondifferentiable minimax fractional programming with generalized convexity. Appl. Math. Comput. 2006, 176:545–551. CrossRef
- Ahmad I, Husain Z: Optimality conditions and duality in nondifferentiable minimax fractional programming with generalized convexity. J. Optim. Theory Appl. 2006, 129:255–275. CrossRef
- Chandra S, Kumar V: Duality in fractional minimax programming problem. J. Aust. Math. Soc. A 1995, 58:376–386. CrossRef
- Husain Z, Ahmad I, Sharma S: Second order duality for minmax fractional programming. Optim. Lett. 2009, 3:277–286. CrossRef
- Hu Q, Chen Y, Jian J: Second-order duality for non-differentiable minimax fractional programming. Int. J. Comput. Math. 2012, 89:11–16. CrossRef
- Hu Q, Yang G, Jian J: On second order duality for minimax fractional programming. Nonlinear Anal. 2011, 12:3509–3514. CrossRef
- Jayswal A: Non-differentiable minimax fractional programming with generalized α -univexity. J. Comput. Appl. Math. 2008, 214:121–135. CrossRef
- Lai HC, Lee JC: On duality theorems for a nondifferentiable minimax fractional programming. J. Comput. Appl. Math. 2002, 146:115–126. CrossRef
- Lai HC, Liu JC, Tanaka K: Necessary and sufficient conditions for minimax fractional programming. J. Math. Anal. Appl. 1999, 230:311–328. CrossRef
- Liu JC, Wu CS: On minimax fractional optimality conditions with invexity. J. Math. Anal. Appl. 1998, 219:21–35. CrossRef
- Liu JC, Wu CS, Sheu RL: Duality for fractional minimax programming. Optimization 1997, 41:117–133. CrossRef
- Sharma S, Gulati TR: Second order duality in minmax fractional programming with generalized univexity. J. Glob. Optim. 2012, 52:161–169. CrossRef
- Yang XM, Hou SH: On minimax fractional optimality and duality with generalized convexity. J. Glob. Optim. 2005, 31:235–252. CrossRef
- Du D-Z, Pardalos PM: Minimax and Applications. Kluwer Academic, Dordrecht; 1995. CrossRef
- Mangasarian OL: Second- and higher-order duality in nonlinear programming. J. Math. Anal. Appl. 1975, 51:607–620. CrossRef
- Hanson MA: Second order invexity and duality in mathematical programming. Opsearch 1993, 30:311–320.
- Second-order duality for a nondifferentiable minimax fractional programming under generalized α-univexity
- Open Access
- Available under Open Access This content is freely available online to anyone, anywhere at any time.
Journal of Inequalities and Applications
- Online Date
- August 2012
- Online ISSN
- Springer International Publishing AG
- Additional Links
- minimax programming
- fractional programming
- nondifferentiable programming
- second-order duality