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Bregman Three-Operator Splitting Methods

Author

Listed:
  • Xin Jiang

    (University of California, Los Angeles)

  • Lieven Vandenberghe

    (University of California, Los Angeles)

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.

Suggested Citation

  • Xin Jiang & Lieven Vandenberghe, 2023. "Bregman Three-Operator Splitting Methods," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 936-972, March.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:3:d:10.1007_s10957-022-02125-9
    DOI: 10.1007/s10957-022-02125-9
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    References listed on IDEAS

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