Linear convergence of the generalized Douglas–Rachford algorithm for feasibility problems

Minh N. Dao () and Hung M. Phan ()
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Minh N. Dao: University of Newcastle
Hung M. Phan: University of Massachusetts Lowell

Journal of Global Optimization, 2018, vol. 72, issue 3, No 4, 443-474

Abstract: Abstract In this paper, we study the generalized Douglas–Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas–Rachford algorithm and the alternating projection algorithm. Specifically, we establish several local linear convergence results for the algorithm in solving feasibility problems with finitely many closed possibly nonconvex sets under different assumptions. Our findings not only relax some regularity conditions but also improve linear convergence rates in the literature. In the presence of convexity, the linear convergence is global.

Keywords: Affine-hull regularity; Cyclic algorithm; Generalized Douglas–Rachford algorithm; Linear convergence; Linear regularity; Strong regularity; Superregularity; Quasi Fejér monotonicity; Quasi coercivity; Primary 47H10; 49M27; Secondary 41A25; 65K05; 65K10; 90C26 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10898-018-0654-x

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