THE BREGMAN PROXIMAL AVERAGE

• Main Authors: Bauschke, H.H (Author), Wang, X. (Author)
• Format: Article
• Language: English
• Published: Society for Industrial and Applied Mathematics Publications 2022
• Subjects: Bounded function; Bregman; Bregman distance; Bregman distances; Bregman envelope; Bregman proximal average; Bregman proximal mapping; Combettes-reye anisotropic envelope; Combettes-reye proximal mapping; Combettes-Reyes anisotropic envelope; Combettes-Reyes proximal mapping; epi-convergence; Epi-convergence; Legendre function; Legendre's functions; Mapping; Proximal mapping; Variational techniques; Φ -prox-bounded function; ϕ -prox-bounded function
• Online Access: View Fulltext in Publisher
• ISBN: 10526234 (ISSN)
• ISSN: 10526234 (ISSN)
• DOI: 10.1137/21M1442474

We provide a proximal average with respect to a 1-coercive Legendre function. In the sense of Bregman distance, the Bregman envelope of the proximal average is a convex combination of Bregman envelopes of individual functions. The Bregman proximal mapping of the average is a convex combination of convexified proximal mappings of individual functions. Techniques from variational analysis provide the keys for the Bregman proximal average. © 2022 Society for Industrial and Applied Mathematics