Alternating projections and coupling slope
Dmitriy Drusvyatskiy, Alexander Davidovich Ioffe, Adrian S. Lewis · arXiv (Cornell University) · 2014
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 transver-sal 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. Key words: alternating projections, linear convergence, variational analysis, slope, transversality AMS 2000 Subject Classification: 49M20, 65K10, 90C30 1