A new projection method for finding the closest point in the intersection of convex sets

Abstract

In this paper we present a new iterative projection method for finding the closest point in the intersection of convex sets to any arbitrary 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 for finding the closest point in the intersection of pairs of finite dimensional subspaces.

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Cited by in corpus (3)

• Computing the resolvent of the sum of maximally monotone operators with the averaged alternating modified reflections algorithm
• Optimal rates of linear convergence of the averaged alternating modified reflections method for two subspaces
• Coordinate-Update Algorithms can Efficiently Detect Infeasible Optimization Problems