Tobias Gerlach In this paper, we study several classes of set-valued maps, which can be used in set-valued optimization and its applications, and their respective maximum and minimum value functions. The definitions of these maps are based on scalar-valued, vector-valued, and cone-valued maps. Moreover, we consider those extremal value functions which are obtained when optimizing linear functionals … Read more
We study different classes of convex and quasiconvex set-valued maps defined by means of the lower-less order relation and the upper-less order relation. The aim of this paper is to formulate necessary and especially sufficient conditions for the convexity/quasiconvexity of extremal value functions. Citation DOI: 10.23952/asvao.3.2021.3.04 Article Download View On convexity and quasiconvexity of extremal … Read more
Set optimization with the set approach has recently gained increasing interest due to its practical relevance. In this problem class one studies optimization problems with a set-valued objective map and defines optimality based on a direct comparison of the images of the objective function, which are sets here. Meanwhile, in the literature a wide range … Read more
In vector optimization with a variable ordering structure the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications it was started to develop a comprehensive theory for these vector optimization problems. Thereby also notions of proper efficiency … Read more