On the optimality conditions of vector-valued \(n\)-set functions (Q1189678)

In a finite atomless measure space \((X,\Gamma,\mu)\), the optimization problem of vector-valued \(n\)-set functions defined on a convex subfamily \(S\) of \(\Gamma^ n=\Gamma\times\cdots\times \Gamma\) is investigated. Necessary and sufficient conditions for a Pareto optimal solution or a proper \(\mathbb{R}^ p_ +\)-solution of the optimization problem with differentiable vector-valued \(n\)-set functions are given.