On the Kolmogorov-Smirnov test for the Poisson distribution with unknown parameter

A number of sufficient optimality theorems are proved for a certain minmax programming problem under a variety of bectovexity (generalized bectovexity) assumptions on the functions involved in the objective and the constraints. A dual is presented for such a problem and duality theorems relating the primal and the dual are proved. It is shown that the dual for certain minmax (generalized) fractional programming problem is a special case of the main problem considered in the paper.