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.

中文翻译：

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Bregman前向后向运算符拆分

我们为自反Banach空间中两个单调算子的和建立了基于Bregman距离的前向后拆分算法的收敛性。即使在欧几里得空间中，到目前为止，仅在最小化问题的情况下，才证明了该算法的收敛性。提出的框架具有Bregman距离随迭代而变化的特征，并且对单值运算符具有新颖的假设，该假设捕获了文献中散布的各种属性。在最小化设置中，我们获得比现有利率更高的利率。