Second-order duality for non-differentiable minimax fractional programming

Abstract

In this paper, a second-order duality for a non-differentiable minimax fractional programming is formulated by generalizing the one developed by Husian et al. [Second order duality for minimax fractional programming, Optim. Lett. 3 (2009), pp. 277–286], for the minimax fractional programming. The weak, strong and strict converse duality theorems are proved for these programs under generalized η-bonvexity assumptions.

Keywords:

• minimax programming
• fractional programming
• second-order duality
• η-bonvexity
• non-differentiable

2000 AMS Subject Classifications :

• 49N15
• 90C30

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11171250) and the Scientific Research Fund of Hunan Provincial Education Department, China (No. 09C565 and 11C0737).