General convergence rates and iterate convergence for R-BPG

Establish convergence rates and convergence of the iterates for the right Bregman proximal gradient algorithm in the general convex composite optimization setting.

Background

The paper introduces right Bregman proximal gradient (R-BPG) by applying Bregman proximal gradient in mirror coordinates and rewriting the resulting method in the original variables. Under suitable assumptions, the authors prove objective monotonicity for general convex composite objectives and obtain an $\mathcal{O}(1/k)$ function-value rate in the specialized Poisson inverse-problem setting with weighted negative entropy.

The general analysis does not establish either convergence rates or convergence of the iterates for the broader convex setting. The authors identify completing these guarantees as a direction for future work, beyond the results proved in the paper.