Prox-regular sets and Legendre-Fenchel transform related to separation properties. (3rd July 2022)

• Record Type: Journal Article
• Authors: Adly, Samir; Nacry, Florent; Thibault, Lionel
• Is Part Of: Optimization. Volume 71:Number 7(2022)
• Page Start: 2097
• Page End: 2129
• Publication Date: 2022-07-03
• Subjects: Prox-regular set -- strongly convex set -- Legendre-Fenchel transform -- semiconvexity -- geometric separation; 49J52 -- 49J53 -- 46N10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1852404
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This paper is devoted to nonconvex/prox-regular separations of sets in Hilbert spaces. We introduce the Legendre-Fenchel r -conjugate of a prescribed function and r -quadratic support functionals and points of a given set, all associated to a positive constant r . By means of these concepts we obtain nonlinear functional separations for points and prox-regular sets. In addition to such functional separations, we also establish geometric separation results with balls for a prox-regular set and a strongly convex set.