  Circumcenters play an important role in the design and analysis of
accelerating various iterative methods in optimization. In this work, we
propose Bregman (pseudo-)circumcenters associated with finite sets. We show the
existence and give explicit formulae for the unique backward and forward
Bregman pseudo-circumcenters of finite sets. Moreover, we use duality to
establish connections between backward and forward Bregman
(pseudo-)circumcenters. Various examples are presented to illustrate the
backward and forward Bregman (pseudo-)circumcenters of finite sets. Our general
framework for circumcenters paves the way for the development of accelerating
iterative methods by Bregman circumcenters.

Optimization and Control