Alternating projections on manifolds

Adrian Lewis (aslewisorie.cornell.edu)
Jerome Malick (jerome.malickinria.fr)

Abstract: We prove that if two smooth manifolds intersect transversally, then the method of alternating projections converges locally at a linear rate. We bound the speed of convergence in terms of the angle between the manifolds, which in turn we relate to the modulus of metric regularity for the intersection problem, a natural measure of conditioning. We discuss a variety of problem classes where the projections are computationally tractable, and we illustrate the method numerically on a problem of finding a low-rank solution of a matrix equation.

Keywords: alternating projections, nonconvex, linear convergence, subspace angle, metric regularity, low-rank approximation, spectral set

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: School of ORIE, Cornell University, July 2006

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Entry Submitted: 07/27/2006
Entry Accepted: 07/27/2006
Entry Last Modified: 07/27/2006

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