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arXiv · 2104.03234

Bregman circumcenters: basic theory

Hui Ouyang·Xianfu Wang
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Abstract

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.

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Hui Ouyang, Xianfu Wang. 2021-04-07. Bregman circumcenters: basic theory. https://arxiv.org/abs/2104.03234

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