On nondifferentiable fractional minimax programming

Necessary and sufficient optimality conditions are derived for a nondifferentiable fractional minimax programming problem: (xepsilonRn) Minimize [(yepsilonY) sup {(f (x, y) + (x(T)Bx)(1/2))/(h(x,y) - (x(T)Dx)(1/2))}] subject to g(x) less than or equal to 0, where Y is a compact subset of R-n; f (. , .) : R-n x R-m --> R and h(. , .) : R-n x R-m --> R are C-1 on R-n x R-m ; g(.) : R-n --> R-r is C-1 on R-n; B and D are n x n symmetric positive semidefinite matrices. For this class of problems, two duals are proposed and weak, strong and strict converse duality theorems are established for each dual problem. (C) 2003 Published by Elsevier B.V.