Shadow Douglas–Rachford Splitting for Monotone Inclusions

By Ernö Robert Csetnek, Yura Malitsky, Matthew K. Tam. Applied Mathematics and Optimization, 2019

65 citations recorded by the source corpus.

In this work, we propose a new algorithm for finding a zero of the sum of two monotone operators where one is assumed to be single-valued and Lipschitz continuous. This algorithm naturally arises from a non-standard discretization of a continuous dynamical system associated with the Douglas–Rachford splitting algorithm. More precisely, it is obtained by performing an explicit, rather than implicit, discretization with respect to one of the operators involved. Each iteration of the proposed algorithm requires the evaluation of one forward and one backward operator.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1416acc648f3dbaa0ac44951d821eadf7df4097e

Citations in the corpus

• ODE Analysis of Stochastic Gradient Methods with Optimism and Anchoring for Minimax Problems and GANs (2019, unknown): “…classical techniques used for the analyses of this work, the stochastic approximation technique [12, 22], ideas from control theory [22, 45], ideas from variational inequalities and monotone operator theory [16, 17], and continuous-time ODE analysis [22, 7], have been utilized for analyzing GANs.”