Abstract
We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has so far been proved only in the case of minimization problems. The proposed framework features Bregman distances that vary over the iterations and a novel assumption on the single-valued operator that captures various properties scattered in the literature. In the minimization setting, we obtain rates that are sharper than existing ones.
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Dedicated to Terry Rockafellar on the occasion of his 85th birthday
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This work was supported by the National Science Foundation under grant DMS-1818946.
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Bùi, M.N., Combettes, P.L. Bregman Forward-Backward Operator Splitting. Set-Valued Var. Anal 29, 583–603 (2021). https://doi.org/10.1007/s11228-020-00563-z
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DOI: https://doi.org/10.1007/s11228-020-00563-z