Optimality conditions and duality for constrained measurable subset selection problems with minmax objective functions

Necessary conditions and sufficient conditions of optimality and several duality results are established under generalized ρ-convexity assumptions for constrained measurable subset selection problems with discrete minmax fractional objective functions. As byproducts of these results, one also obtains similar optimality and duality criteria for three additional classes of problems with discrete minmax, fractional, and ordinary objective functions, which are special cases of the main problem studied in this paper.