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

Daniel O'Connor(daniel.v.oconnor***at***gmail.com)
Lieven Vandenberghe(vandenbe***at***ucla.edu)

Abstract: 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.

Keywords: Douglas-Rachford splitting, primal-dual algorithms, monotone operators, proximal algorithms

Category 1: Convex and Nonsmooth Optimization


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Entry Submitted: 10/05/2017
Entry Accepted: 10/05/2017
Entry Last Modified: 10/05/2017

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