Set-valued increasing-along-rays maps and well-posed set-valued star-shaped optimization

In this paper we introduce a class of set-valued increasing-along-rays maps and present some properties of set-valued increasing-along-rays maps. We show that the increasing-along-rays property of a set-valued map is close related to the corresponding set-valued star-shaped optimization. By means of increasing-along-rays property, we investigate stability and well-posedness of set-valued star-shaped optimization.