F. J. Aragón Artacho, R. Campoy García

The family of projection methods is a wide class of algorithms which are successfully used for finding common points of a collection of sets. They iterate by computing projections onto the individual sets, rather than dealing with the intersection itself. In this paper we present a new iterative projection method for finding the closest point in the intersection of convex sets to any given point in a Hilbert space. This method, termed AAMR for averaged alternating modified reflections, can be viewed as an adequate modification of the Douglas–Rachford method that yields a solution to the best approximation problem. Under a constraint qualification at the point of interest, we show strong convergence of the method. In fact, the so-called strong CHIP fully characterizes the convergence of the AAMR method for every point in the space. We report some promising numerical experiments where we compare the performance of AAMR against other projection methods.

Keywords: Best approximation, Projection, Douglas–Rachford algorithm, Feasibility problem


RM-1 Ramiro Melendreras Award
September 3, 2019  4:50 PM
I3L1. Georgina Blanes building

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