On optimality and duality theorems of nonlinear disjunctive fractional minmax programs

This paper is concerned with the study of optimality conditions for disjunctive fractional minmax programming problems in which the decision set can be considered as a union of a family of convex sets. Dinkelbach’s global optimization approach for finding the global maximum of the fractional programming problem is discussed. Using the Lagrangian function definition for this type of problem, the Kuhn–Tucker saddle point and stationary-point problems are established. In addition, via the concepts of Mond–Weir type duality and Schaible type duality, a general dual problem is formulated and some weak, strong and converse duality theorems are proven.