Infeasibility and Error Bound Imply Finite Convergence of Alternating Projections

Convergence and Error Bound

Convergence Analysis of Alternating Nonconvex Projections

We consider the convergence properties for alternating projection algorithm (a.k.a alternating projections) which has been widely utilized to solve many practical problems in machine learning, signal and image processing, communication and statistics since it is a gradient-free method (without requiring tuning the step size) and it usually converges fast for solving practical problems. Although...

Local Linear Convergence for Alternating and Averaged Nonconvex Projections

The idea of a finite collection of closed sets having “linearly regular intersection” at a point is crucial in variational analysis. This central theoretical condition also has striking algorithmic consequences: in the case of two sets, one of which satisfies a further regularity condition (convexity or smoothness for example), we prove that von Neumann’s method of “alternating projections” con...

Local convergence for alternating and averaged nonconvex projections

The idea of a finite collection of closed sets having “strongly regular intersection” at a given point is crucial in variational analysis. We show that this central theoretical tool also has striking algorithmic consequences. Specifically, we consider the case of two sets, one of which we assume to be suitably “regular” (special cases being convex sets, smooth manifolds, or feasible regions sat...

On Local Convergence of the Method of Alternating Projections

The method of alternating projections is a classical tool to solve feasibility problems. Here we prove local convergence of alternating projections between subanalytic sets A,B under a mild regularity hypothesis on one of the sets. We show that the speed of convergence is O(k−ρ) for some ρ ∈ (0,∞).