Duality on a nondifferentiable minimax fractional programming

We establish the necessary and sufficient optimality conditions on a nondifferentiable minimax fractional programming problem. Subsequently, applying the optimality conditions, we constitute two dual models: Mond-Weir type and Wolfe type. On these duality types, we prove three duality theorems—weak duality theorem, strong duality theorem, and strict converse duality theorem.

[1]  W. Schmitendorf.  Necessary conditions and sufficient conditions for static minmax problems , 1977 .

[2]  S. Chandra,et al.  Duality in fractional minimax programming , 1995, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[3]  R. N. Mukherjee,et al.  Duality for fractional minimax programming problems , 1990, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[4]  K Fan,et al.  Minimax Theorems. , 1953, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Panos M. Pardalos,et al.  Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems , 2001 .

[6]  Izhar Ahmad,et al.  Second order duality for minmax fractional programming , 2009, Optim. Lett..

[7]  Siegfried Schaible,et al.  Complex Minimax Fractional Programming of Analytic Functions , 2008 .

[8]  J. Neumann.  A Model of General Economic Equilibrium , 1945 .

[9]  Kensuke Tanaka,et al.  Necessary and sufficient conditions for minimax fractional programming , 1999 .

[10]  Shinji Tanimoto.  Duality for a class of nondifferentiable mathematical programming problems , 1981 .

[11]  J. C. Lee,et al.  On duality theorems for a nondifferentiable minimax fractional programming , 2002 .

[12]  Jin-Bao Jian,et al.  On second order duality for minimax fractional programming , 2011 .

[13]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[14]  Alexander Schönhuth,et al.  A fractional programming approach to efficient DNA melting temperature calculation , 2005, Bioinform..

[15]  P. Pardalos,et al.  Minimax and applications , 1995 .

[16]  S. Schaible,et al.  Complex Fractional Programming and the Charnes-Cooper Transformation , 2005 .

[17]  Izhar Ahmad,et al.  Optimality Conditions and Duality in Nondifferentiable Minimax Fractional Programming with Generalized Convexity , 2006 .

[18]  Shu-Cherng Fang,et al.  Global optimization for a class of fractional programming problems , 2009, J. Glob. Optim..