Bregman Three-Operator Splitting Methods

Xin Jiang () and Lieven Vandenberghe ()
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Xin Jiang: University of California, Los Angeles
Lieven Vandenberghe: University of California, Los Angeles

Journal of Optimization Theory and Applications, 2023, vol. 196, issue 3, No 7, 936-972

Abstract: Abstract The paper presents primal–dual proximal splitting methods for convex optimization, in which generalized Bregman distances are used to define the primal and dual proximal update steps. The methods extend the primal and dual Condat–Vũ algorithms and the primal–dual three-operator (PD3O) algorithm. The Bregman extensions of the Condat–Vũ algorithms are derived from the Bregman proximal point method applied to a monotone inclusion problem. Based on this interpretation, a unified framework for the convergence analysis of the two methods is presented. We also introduce a line search procedure for stepsize selection in the Bregman dual Condat–Vũ algorithm applied to equality-constrained problems. Finally, we propose a Bregman extension of PD3O and analyze its convergence.

Keywords: First-order proximal splitting algorithm; Bregman divergence; 49M29; 90C06; 90C25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-022-02125-9

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