A Bregman proximal point algorithm without convexity in Banach spaces

ABSTRACT

In this paper, we first introduce a Bregman prox-convexity notion as the generalization of the convexity for Bregman prox-convexity in Banach spaces. We verify the single-valudeness and Bregman firm nonexpansiveness of the Bregman proximity operator of the functions and provide examples of the notion. Using this notion, we show that the Bregman proximal point scheme remains convergent under appropriate conditions on the functions to be minimized in the setting of Banach spaces.

KEYWORDS:

• Bregman distance
• nonconvex optimization
• Bregman proximal point algorithm
• Bregman prox-convexity
• Bregman generalized convex function

Disclosure statement

No potential conflict of interest was reported by the author(s).