Bregman Circumcenters: Basic Theory

Hui Ouyang () and Xianfu Wang ()
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Hui Ouyang: University of British Columbia
Xianfu Wang: University of British Columbia

Journal of Optimization Theory and Applications, 2021, vol. 191, issue 1, No 10, 252-280

Abstract: 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 of 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.

Keywords: Bregman distance; Legendre function; Backward Bregman projection; Forward Bregman projection; Backward Bregman (pseudo-)circumcenter; Forward Bregman (pseudo-)circumcenter; 90C48; 47H04; 47H05; 90C25; 52A41 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-021-01937-5

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