The ANZIAM Journal

Research Article

Minimax fractional programming involving generalised invex functions

H. C. Laia1 and J. C. Liua2

a1 Department of Applied Mathematics, Chung Yuang Christian University, Chung Li 320, Taiwan; e-mail: hclai@cycu.edu.tw.

a2 Section of Mathematics, National Overseas Chinese Student University, Linkou 24499 PO Box 1-1337, Taiwan.

Abstract

The convexity assumptions for a minimax fractional programming problem of variational type are relaxed to those of a generalised invexity situation. Sufficient optimality conditions are established under some specific assumptions. Employing the existence of a solution for the minimax variational fractional problem, three dual models, the Wolfe type dual, the Mond-Weir type dual and a one parameter dual type, are constructed. Several duality theorems concerning weak, strong and strict converse duality under the framework of invexity are proved.

(Received January 05 1999)

(Revised October 30 2000)