标题： 原始对偶分裂算法用于求解包含复合、利普希茨和并行和单调算子混合的包含问题 显示英文标题

标题： Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum monotone operators

摘要： 我们提出了一种原始-对偶分裂算法，用于求解涉及集值和利普希茨算子的和、线性复合以及并行和的单调包含问题。 该算法的一个重要特点是，在公式中出现的利普希茨算子可以通过显式步骤单独处理，而集值算子则通过它们的预解算子单独处理。 此外，该算法具有高度并行性，因为其大部分步骤可以同时执行。 这项工作汇集并显著扩展了各种结构化单调包含问题及其求解方法。 特别关注其在凸最优化问题中的应用。 显示英文摘要

摘要： We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An important feature of the algorithm is that the Lipschitzian operators present in the formulation can be processed individually via explicit steps, while the set-valued operators are processed individually via their resolvents. In addition, the algorithm is highly parallel in that most of its steps can be executed simultaneously. This work brings together and notably extends various types of structured monotone inclusion problems and their solution methods. The application to convex minimization problems is given special attention.