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In this paper, we extend the previous convergence results for the generalizedalternating projection method applied to subspaces in [arXiv:1703.10547] tohold also for smooth manifolds. We show that the algorithm locally behavessimilarly in the subspace and manifold settings and that the same rates areobtained. We also present convergence rate results for when the algorithm isapplied to non-empty, closed, and convex sets. The results are based on afinite identification property that implies that the algorithm after an initialidentification phase solves a smooth manifold feasibility problem. Therefore,the rates in this paper hold asymptotically for problems in which thisidentification property is satisfied. We present a few examples where this isthe case and also a counter example for when this is not.

Generalized Alternating Projections on Manifolds and Convex Sets