4 research outputs found
A Note on the Finite Convergence of Alternating Projections
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.Comment: 9 pages, 7 figure
A polynomial projection-type algorithm for linear programming
We propose a simple O([n5/logn]L)O([n5/logn]L) algorithm for linear programming feasibility, that can be considered as a polynomial-time implementation of the relaxation method. Our work draws from Chubanov’s “Divide-and-Conquer” algorithm (Chubanov, 2012), with the recursion replaced by a simple and more efficient iterative method. A similar approach was used in a more recent paper of Chubanov (2013)