Linear convergence of the Douglas–Rachford method for two closed sets. (1st February 2016)

• Record Type: Journal Article
• Authors: Phan, Hung M.
• Is Part Of: Optimization. Volume 65:Number 2(2016)
• Page Start: 369
• Page End: 385
• Publication Date: 2016-02-01
• Subjects: affine-hull reduction -- Douglas–Rachford method -- Fejér monotonicity -- R-linear convergence -- linear regularity -- strong regularity -- superregularity; Primary: 49M27 -- 65K10 -- Secondary: 47H09 -- 49J52 -- 49M37 -- 65K05 -- 90C26; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2015.1051532
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we investigate the Douglas–Rachford method (DR) for two closed (possibly nonconvex) sets in Euclidean spaces. We show that under certain regularity conditions, the DR converges locally with -linear rate. In convex settings, we prove that the linear convergence is global. Our study recovers recent results on the same topic.