On necessary conditions for a class of nondifferentiable minimax fractional programming

The Kuhn-Tucker-type necessary optimality conditions are given for the problem of minimizing a max fractional function, where the numerator of the function involved is the sum of a differentiable function and a convex function while the denominator is the difference of a differentiable function and a convex function, subject to a set of differentiable nonlinear inequalities on a convex subset C of Rn, under the conditions similar to the Kuhn-Tucker constraint qualification or the Arrow-Hurwicz-Uzawa constraint qualification or the Abadie constraint qualification. Relations with the calmness constraint qualification are given.