Đối ngẫu bậc hai cho bài toán lập trình phân số minmax

Ahmad I.: Optimality conditions and duality in fractional minimax programming involving generalized ρ−invexity. Inter. J. Manag. Syst. 19, 165–180 (2003) Ahmad I., Husain Z.: Optimality conditions and duality in nondifferentiable minimax fractional programming with generalized convexity. J. Optim. Theory Appl. 129, 255–275 (2006) Ahmad I., Husain Z.: Second order (F, α, ρ, d)-convexity and duality in multiobjective programming. Inform. Sci. 176, 3094–3103 (2006) Ahmad I., Husain Z., Sharma S.: Second-order duality in nondifferentiable minmax programming involving type-I functions. J. Comput. Appl. Math. 215, 91–102 (2008) Bajona-Xandri C., Martinez-Legaz J.E.: Lower subdifferentiability in minimax fractional programming. Optimization 45, 1–12 (1999) Barrodale I.: Best rational approximation and strict quasiconvexity. SIAM J. Numer. Anal. 10, 8–12 (1973) Bector C.R., Chandra S.: Generalized-bonvexity and higher order duality for fractional programming. Opsearch 24, 143–154 (1987) Bector C.R., Chandra S., Husain I.: Second order duality for a minimax programming problem. Opsearch 28, 249–263 (1991) Chandra S., Kumar V.: Duality in fractional minimax programming. J. Aust. Math. Soc. Ser. A 58, 376–386 (1995) Hanson M.A.: Second order invexity and duality in mathematical programming. Opsearch 30, 313–320 (1993) Jayswal A.: Nondifferentiable minimax fractional programming with generalized α-univexity. J. Comput. Appl. Math. 214, 121–135 (2008) Lai H.C., Lee J.C.: On duality theorems for a nondifferentiable minimax fractional programming. J. Comput. Appl. Math. 146, 115–126 (2002) Lai H.C., Liu J.C., Tanaka K.: Necessary and sufficient conditions for minimax fractional programming. J. Math. Anal. Appl. 230, 311–328 (1999) Liu J.C.: Second order duality for minimax programming. Util. Math. 56, 53–63 (1999) Liu J.C., Wu C.S.: On minimax fractional optimality conditions with invexity. J. Math. Anal. Appl. 219, 21–35 (1998) Liu J.C., Wu C.S.: On minimax fractional optimality conditions with (F, ρ)-convexity. J. Math. Anal. Appl. 219, 36–51 (1998) Liu J.C., Wu C.S., Sheu R.L.: Duality for fractional minmax programming. Optimization 41, 117–133 (1997) Mangasarian O.L.: Second and higher order duality in nonlinear programming. J. Math. Anal. Appl. 51, 607–620 (1975) Mishra S.K., Wang S.Y., Lai K.K., Shi J.M.: Nondifferentiable minimax fractional programming under generalized univexity. J. Comput. Appl. Math. 158, 379–395 (2003) Mond B.: Second order duality for nonlinear programs. Opsearch 11, 90–99 (1974) Pandey S.: Duality for multiobjective fractional programming involving generalized η-bonvex functions. Opsearch 28, 36–43 (1991) Schroeder R.G.: Linear programming solutions to ratio games. Oper. Res. 18, 300–305 (1970) Soyster A.L., Lev B., Loof D.: Conservative linear programming with mixed multiple objectives. Omega 5, 193–205 (1977) Yadav S.R., Mukherjee R.N.: Duality for fractional minimax programming problems. J. Aust. Math. Soc. Ser. B 31, 484–492 (1990) Yang X.M., Hou S.H.: On minimax fractional optimality and duality with generalized convexity. J. Global Optim. 31, 235–252 (2005)