On constrained set-valued optimization

The set-valued optimization problem min(C) F(x), G(x) boolean AND (-K) not equal empty set, is considered, where F : R(n) -> R(m) and G : R(n) -> R(p) are set-valued functions, and C subset of R(m) and K C RP are closed convex cones. Two type of solutions, called w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers), are treated. In terms of the Dini set-valued directional derivative first-order necessary conditions for a point to be a w-minimizer, and first-order sufficient conditions for a point to be an i-minimizer are established, both in primal and dual form.