Linear and strong convergence of algorithms involving averaged nonexpansive operators

By Heinz H. Bauschke, Dominikus Noll, Hung M. Phan. Journal of Mathematical Analysis and Applications, 2014

93 citations recorded by the source corpus.

We introduce regularity notions for averaged nonexpansive operators. Combined with regularity notions of their fixed point sets, we obtain linear and strong convergence results for quasicyclic, cyclic, and random iterations. New convergence results on the Borwein-Tam method (BTM) and on the cylically anchored Douglas-Rachford algorithm (CADRA) are also presented. Finally, we provide a numerical comparison of BTM, CADRA and the classical method of cyclic projections for solving convex feasibility problems.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/4079fb16cfd330ab4b7270f3ebaf8840c4fa23ad

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Citations in the corpus

Outer approximation methods for solving variational inequalities in Hilbert space (2017, background): “[42] while the term ‘weakly regular’ can be found in Kolobov et al.”
Linear convergence of the Douglas–Rachford method for two closed sets (2014, unknown): “This result is also re-established in [10, Section 4] within the context of averaged nonexpansive operators.”
SURVEY: SIXTY YEARS OF DOUGLAS–RACHFORD (2018, methodology): “Bauschke, Noll and Phan provided linear convergence results for the Borwein–Tam method in the finite-dimensional case in the presence of transversality [39].”