Variable Stepsize Distributed Forward-Backward Splitting Methods as Relocated Fixed-Point Iterations

Felipe Atenas; Minh N. Dao; Matthew K. Tam

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arXiv · 2601.15531

Variable Stepsize Distributed Forward-Backward Splitting Methods as Relocated Fixed-Point Iterations

Felipe Atenas·Minh N. Dao·Matthew K. Tam

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Abstract

We present a family of distributed forward-backward methods with variable stepsizes to find a solution of structured monotone inclusion problems. The framework is constructed by means of relocated fixed-point iterations, extending the approach introduced in arXiv:2507.07428 to conically averaged operators, thus including iteration operators for methods of forward-backward type devised by graphs. The family of methods we construct preserve the per-iteration computational cost and the convergence properties of their constant stepsize counterparts. Specifically, we show that the resulting methods generate a sequence that converges to a fixed-point of the underlying iteration operator, whose shadow sequences converge to a solution of the problem. Numerical experiments illustrate the behaviour of our framework in structured sparse optimisation problems.

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BibTeX RIS

Felipe Atenas, Minh N. Dao, Matthew K. Tam. 2026-01-21. Variable Stepsize Distributed Forward-Backward Splitting Methods as Relocated Fixed-Point Iterations. https://arxiv.org/abs/2601.15531

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