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Modifying the Douglas-Rachford algorithm to solve best approximation problems

Banff International Research Station for Mathematical Innovation and Discovery

In this talk 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 AAMR for every point in the space. We show 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.
This talk is based on a joint work with Rubén Campoy.

Mathematics; Operations research, mathematical programming; Operator theory; Control/optimization/operation research

video/mp4

Author affiliation: Alicante

2018-03-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64938

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/