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

Francisco J. Aragón Artacho () and Rubén Campoy ()
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Francisco J. Aragón Artacho: University of Alicante
Rubén Campoy: University of Alicante

Computational Optimization and Applications, 2018, vol. 69, issue 1, No 5, 99-132

Abstract: 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.

Keywords: Best approximation problem; Convex set; Projection; Reflection; Nonexpansive mapping; Douglas–Rachford algorithm; Feasibility problem; 47H09; 47N10; 90C25 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10589-017-9942-5

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