Ergodic behaviour of a Douglas-Rachford operator away from the origin

2017/08/30 by Jonathan M. Borwein, Borwein, Jonathan M., Ohad Giladi +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Geometric Analysis and Curvature Flows #Numerical methods in inverse problems #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1708.09068

openalex publication_date 2017/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that away from the origin, the Douglas-Rachford operator with respect to a sphere and a convex set in a Hilbert space can be approximated by a another operator which satisfies a weak ergodic theorem. Similar results for other projection and reflection operators are also discussed.

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