Accelerating the alternating projection algorithm for the case of affine subspaces using supporting hyperplanes

2014/06/16 by Pang, C. H. Jeffrey
#11D04 #41A50 #47A46 #47A50 #47J25 #52A20 #90C59 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1406.4012

Abstract

The von Neumann-Halperin method of alternating projections converges strongly to the projection of a given point onto the intersection of finitely many closed affine subspaces. We propose acceleration schemes making use of two ideas: Firstly, each projection onto an affine subspace identifies a hyperplane of codimension 1 containing the intersection, and secondly, it is easy to project onto a finite intersection of such hyperplanes. We give conditions for which our accelerations converge strongly. Finally, we perform numerical experiments to show that these accelerations perform well for a matrix model updating problem.

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