On the equivalence of the primal-dual hybrid gradient method and Douglas-Rachford splitting

• 成果类型: Article
• 署名作者: O'Connor, Daniel; Vandenberghe, Lieven
• 署名单位: University of San Francisco; University of California System; University of California Los Angeles
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-018-1321-1
• 发表日期: 2020
• 页码: 85-108
• 关键词: Convergence analysis; monotone inclusions; algorithm; DECOMPOSITION; optimization; SUM

摘要

The primal-dual hybrid gradient (PDHG) algorithm proposed by Esser, Zhang, and Chan, and by Pock, Cremers, Bischof, and Chambolle is known to include as a special case the Douglas-Rachford splitting algorithm for minimizing the sum of two convex functions. We show that, conversely, the PDHG algorithm can be viewed as a special case of the Douglas-Rachford splitting algorithm.