Applied Set-Valued Analysis and Optimization

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DOI: 10.23952/asvao.6.2024.2.01
Volume 6, Issue 2, 1 August 2024, Pages 113-135

 

Abstract. We propose and study a weakly convergent variant of the forward-backward algorithm for solving structured monotone inclusion problems. Our algorithm features a per-iteration deviation vector, providing additional degrees of freedom. The only requirement on the deviation vector to guarantee convergence is that its norm is bounded by a quantity that can be computed online. This approach offers great flexibility and paves the way for the design of new forward-backward-based algorithms, while still retaining global convergence guarantees. These guarantees include linear convergence under a metric subregularity assumption. Choosing suitable monotone operators enables the incorporation of deviations into other algorithms, such as the Chambolle-Pock method and Krasnosel’skiı̆-Mann iterations. We propose a novel inertial primal-dual algorithm by selecting the deviations along a momentum direction and deciding their size by using the norm condition. Numerical experiments validate our convergence claims and demonstrate that even this simple choice of a deviation vector can enhance the performance compared to, for instance, the standard Chambolle-Pock algorithm.

 
How to Cite this Article:
H. Sadeghi, S. Banert, P. Giselsson, Forward-backward splitting with deviations for monotone inclusions, Appl. Set-Valued Anal. Optim. 6 (2024), 113-135.