On Dykstra's algorithm: finite convergence, stalling, and the method of alternating projections
Optimization and Control
2020-01-22 v1 Numerical Analysis
Numerical Analysis
Abstract
A popular method for finding the projection onto the intersection of two closed convex subsets in Hilbert space is Dykstra's algorithm. In this paper, we provide sufficient conditions for Dykstra's algorithm to converge rapidly, in finitely many steps. We also analyze the behaviour of Dykstra's algorithm applied to a line and a square. This case study reveals stark similarities to the method of alternating projections. Moreover, we show that Dykstra's algorithm may stall for an arbitrarily long time. Finally, we present some open problems.
Cite
@article{arxiv.2001.06747,
title = {On Dykstra's algorithm: finite convergence, stalling, and the method of alternating projections},
author = {Heinz H. Bauschke and Regina S. Burachik and Daniel B. Herman and C. Yalcin Kaya},
journal= {arXiv preprint arXiv:2001.06747},
year = {2020}
}