FORWARD-BACKWARD SPLITTING WITH DEVIATIONS FOR MONOTONE INCLUSIONS

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Sammanfattning

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'skii-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. Copy: 2024 Applied Set-Valued Analysis and Optimization.

Originalspråkengelska
Sidor (från-till)113-135
Antal sidor23
TidskriftApplied Set-Valued Analysis and Optimization
Volym6
Nummer2
DOI
StatusPublished - 2024 aug. 1

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