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Alternating projections and coupling slope

D. Drusvyatskiy(ddrusv***at***uw.edu)
A.D. Ioffe(ioffe***at***math.technion.ac.il)
A.S. Lewis(adrian.lewis***at***cornell.edu)

Abstract: We consider the method of alternating projections for finding a point in the intersection of two possibly nonconvex closed sets. We present a local linear convergence result that makes no regularity assumptions on either set (unlike previous results), while at the same time weakening standard transversal intersection assumptions. The proof grows out of a study of the slope of a natural nonsmooth coupling function. When the two sets are semi-algebraic and bounded, we also prove subsequence convergence to the intersection with no transversality assumption.

Keywords: alternating projections, linear convergence, variational analysis, slope, transversality

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Other Topics (Other )


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Entry Submitted: 01/28/2014
Entry Accepted: 01/28/2014
Entry Last Modified: 01/28/2014

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