Duality for fractional minimax programming problems

Abstract

Abstract Duality theory is discussed for fractional minimax programming problems. Two dual problems are proposed for the minimax fractional problem: minimize max y∈Υ f(x, y)/h(x, y) , subject to g(x) ≤ 0. For each dual problem a duality theorm is established. Mainly these are generalisations of the results of Tanimoto [14] for minimax fractional programming problems. It is noteworthy here that these problems are intimately related to a class of nondifferentiable fractional programming problems.