论文标题
通过缩放的相对图对Davis-Yin分裂的收敛分析
Convergence Analyses of Davis-Yin Splitting via Scaled Relative Graphs
论文作者
论文摘要
Davis-Yin拆分（DYS）在优化方面发现了广泛的应用，但其线性收敛速率尚未得到广泛的研究。缩放的相对图（SRG）通过将操作员的作用映射到复杂平面上，简化了操作员分裂方法的收敛分析，但是先前的SRG理论并未完全适用于DYS运算符。在这项工作中，我们为DYS操作员形式化了SRG理论，并使用它来获得更严格的收缩因素。
Davis-Yin splitting (DYS) has found a wide range of applications in optimization, but its linear rates of convergence have not been studied extensively. The scaled relative graph (SRG) simplifies the convergence analysis of operator splitting methods by mapping the action of the operator onto the complex plane, but the prior SRG theory did not fully apply to the DYS operator. In this work, we formalize an SRG theory for the DYS operator and use it to obtain tighter contraction factors.
