Convex analysis of minimal time and signed minimal time functions. (3rd April 2022)

• Record Type: Journal Article
• Authors: Cuong, D. V.; Mordukhovich, B. S.; Nam, N. M.; Wells, M.
• Is Part Of: Optimization. Volume 71:Number 4(2022)
• Page Start: 849
• Page End: 876
• Publication Date: 2022-04-03
• Subjects: Minimal time and signed minimal time functions -- distance and signed distance functions -- convex and variational analysis -- generalized differentiation; 49J52 -- 49J53 -- 46A55 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1910695
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we first consider the class of minimal time functions in the general setting of locally convex topological vector (LCTV) spaces. The results obtained in this framework are based on a novel notion of the closedness of target sets with respect to constant dynamics. Then, we introduce and investigate a new class of signed minimal time functions, which are generalizations of the signed distance functions. Subdifferential formulas for the signed minimal time and distance functions are obtained under the convexity assumptions on the given data.