SECOND-ORDER RADIAL-ASYMPTOTIC DERIVATIVES AND APPLICATIONS IN SET-VALUED VECTOR OPTIMIZATION

We propose the notion of second-order radial-asymptotic derivatives of a set-valued map, establish some simple calculus rules and apply directly them to obtain optimality conditions for some particular optimization problems. Then, we employ these derivatives together with second-order contingent derivatives to analyze sensitivity for nonsmooth set-valued vector optimization. Properties of second-order contingent derivatives of the proper perturbation maps of a parameterized optimization problem are obtained.