论文标题
在可分离凸优化的预测校正框架中构建分裂收缩算法
On construction of splitting contraction algorithms in a prediction-correction framework for separable convex optimization
论文作者
论文摘要
在过去的十年中，我们开发了一系列的分裂收缩算法，用于可分离的凸优化问题，这是乘数交替方向方法的根源。这些算法的收敛性在特定的模型范围的条件下进行了研究，而这些条件可以在概念上抽象为两个通用条件，而当这些算法均被统一为预测校正框架。在本文中，我们又展示了一种建设性的方式，用于指定通用收敛保证条件，通过该条件可以自动生成新的分裂收缩算法。可以通过指定预测校正框架来设计更多的应用程序分配收缩算法，同时证明其收敛性是例行程序。
In the past decade, we had developed a series of splitting contraction algorithms for separable convex optimization problems, at the root of the alternating direction method of multipliers. Convergence of these algorithms was studied under specific model-tailored conditions, while these conditions can be conceptually abstracted as two generic conditions when these algorithms are all unified as a prediction-correction framework. In this paper, in turn, we showcase a constructive way for specifying the generic convergence-guaranteeing conditions, via which new splitting contraction algorithms can be generated automatically. It becomes possible to design more application-tailored splitting contraction algorithms by specifying the prediction-correction framework, while proving their convergence is a routine.
