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We consider the problem, that has various applications in imaging, of finding a pair of points, in two convex sets, such that the distance between the points is as small as possible. Assuming that the convex sets are polyhedrons, and that the angle between any pair of faces of these polyhedrons is lower bounded by a positive constant, we will describe the local as well as the global convergence rate of a widely-used algorithm that solves this problem: the Douglas-Rachford method.
This presentation is part of Minisymposium “MS65 - Machine learning techniques for image reconstruction (2 parts)”
organized by: Markus Haltmeier (University Innsbruck) , Linh Nguyen (University of Idaho) .