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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.
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J.-B. Baillon and G. Haddad, Quelques propriétés des opérateurs angle-bornés et
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A. Renaud and G. Cohen, An extension of the auxiliary problem principle to nonsymmetric auxiliary operators,
1997
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H. H. Bauschke, J. M. Borwein, and P. L. Combettes, Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces,
2001
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C. Zălinescu,
2002
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H. H. Bauschke, J. M. Borwein, and P. L. Combettes, Bregman monotone optimization algorithms,
2003
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J. M. Borwein and J. D. Vanderwerff,
2010
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P. L. Combettes and Q. V. Nguyen, Solving composite monotone inclusions in reflexive Banach spaces by constructing best Bregman approximations from their Kuhn-Tucker set,
2016
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H. H. Bauschke, J. Bolte, and M. Teboulle, A descent lemma beyond Lipschitz gradient continuity: First-order methods revisited and applications,
2017
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H. H. Bauschke and P. L. Combettes,
2017
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Q. V. Nguyen, Forward-backward splitting with Bregman distances,
2017
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S. Salzo, The variable metric forward-backward splitting algorithm under mild differentiability assumptions,
2017
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H. H. Bauschke, M. N. Dao, and S. B. Lindstrom, Regularizing with Bregman–Moreau envelopes,
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P. L. Combettes and B. C. Vũ, Variable metric quasi-Fejér monotonicity,
2013
Cited alongside, same era.
P. L. Combettes and B. C. Vũ, Variable metric forward-backward splitting with applications to monotone inclusions in duality,
2014
Cited alongside, same era.
2018
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J. Frecon, S. Salzo, and M. Pontil, Bilevel learning of the group lasso structure,
2018
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G. Ortiz-Jiménez, M. El Gheche, E. Simou, H. Petric Maretić, and P. Frossard, Forward-backward splitting for optimal transport based problems,
2020
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