Mixed duality without a constraint qualification for minimax fractional programming

Abstract

Without the need of a constraint qualification, we establish the necessary and sufficient optimality conditions for minimax fractional programming. Using these optimality conditions, we construct a mixed dual model which unifies the Mond–Weir dual, Wolfe dual and a parameter dual models. Several duality theorems are established. Consequently, this article partly solves the problem posed by Lai et al. [H.C. Lai, J.C. Liu and K. Tanaka (1999). Duality without a constraint qualification for minimax fractional programming. Journal of Optimization Theory and Applications, 101, 109–125.].

Keywords:

• Minimax fractional programming
• Optimality conditions
• Cone directions
• Mixed duality
• Mathematics Subject Classifications 2000: 49N15
• 49K35
• 90C32

Acknowledgment

This work was supported by National Natural Science Foundation of China, Grant No. 10231060 and 19971042.

Notes

*E-mail: [email protected]

Additional information

Notes on contributors

Houchun Zhou*

*E-mail: [email protected]