A note on the finite convergence of alternating projections |
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| Institution: | 1. ARC Training Centre for Transforming Maintenance through Data Science, Curtin University, Australia;2. School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Australia;3. School of Mathematics and Statistics, The University of Melbourne, Australia |
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| Abstract: | We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality, which until now has been restricted to sets with nonempty intersection. In the special case of a polyhedron and closed half space, our sufficient conditions define the minimum distance between the two sets that is required for alternating projections to converge in a single iteration. |
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| Keywords: | Alternating projections Proximal normal cone Intrinsic transversality Finite convergence Polyhedrons |
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