A weakly convergent fully inexact Douglas-Rachford method with relative\n error tolerance

2018/09/07 by B. F. Svaiter, Svaiter, Benar F.
Computer Science · Mathematics · #47H05 #49J45 #49M27 #65G99 #65K05 #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1809.02312

openalex publication_date 2018/09/07 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

Abstract

Douglas-Rachford method is a splitting algorithm for finding a zero of the\nsum of two maximal monotone operators. Each of its iterations requires the\nsequential solution of two proximal subproblems. The aim of this work is to\npresent a fully inexact version of Douglas-Rachford method wherein both\nproximal subproblems are solved approximately within a relative error\ntolerance. We also present a semi-inexact variant in which the first subproblem\nis solved exactly and the second one inexactly. We prove that both methods\ngenerate sequences weakly convergent to the solution of the underlying\ninclusion problem, if any.\n

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