Optimality conditions for fractional minmax programming (Q1061017)

Necessary and sufficient conditions are given for the existence of an optimal solution to the fractional minmax programming problem ''Minimize \(F(x)=\sup_{y\in Y}(f(x,y)+(x^ tBx)^{1/2})/h(x,y)\) subject to g(x)\(\leq 0''\), where Y is a compact subset of \(R^ m\), f, g and h are differentiable functions, and \(h(x,y)>0\) for all feasible x, y.