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Volume 5, Issue 1, 1 April 2023, Pages 71-92
Abstract. 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 over the image sets of the set-valued maps. Such extremal value functions play an important role for instance for derivative concepts for set-valued maps or for algorithmic approaches in set-valued optimization. We formulate conditions under which the set-valued maps and their extremal value functions inherit properties like (Lipschitz-)continuity and convexity.
How to Cite this Article:
G. Eichfelder, T. Gerlach, S. Rocktäschel, Convexity and continuity of specific set-valued maps and their extremal value functions, J. Appl. Numer. Optim. 5 (2023), 71-92.