Higher-order weak radial epiderivatives and non-convex set-valued optimization problems
Qilin Wang, He Liu, Shengjie Li · Journal of Industrial and Management Optimization · 2018
In the paper, we propose the notion of the higher-order weak radial epiderivative of a set-valued map, and discuss some of its properties. Then, by virtue of the higher-order weak radial epiderivative, we establish the optimality necessary conditions and sufficient ones of weak efficient solutions (Pareto efficient solutions) for non-convex set-valued optimization problems. Some of the obtained results improve and extend the recent existing results. Several examples are provided to show the main results obtained.