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- Local Linear Convergence for Alternating and Averaged Nonconvex Projections
As a consequence, in the case of several arbitrary closed sets having linearly regular intersection at some point, the method of “averaged projections” converges locally at a linear rate to a point in the intersection Inexact versions of both algorithms also converge linearly
- Local Linear Convergence for Alternating and Averaged Nonconvex Projections
Our algorithmic contribution is to show that assuming linear regularity, local linear convergence does not depend on convexity of both sets, but rather on a good geometric property (such as convexity, smoothness, or more generally, “amenability” or “prox-regularity”) of just one of the two
- Local convergence for alternating and averaged nonconvex projections
We then prove that von Neumann's method of "alternating projections" converges locally to a point in the intersection, at a linear rate associated with a modulus of regularity
- Local linear convergence of alternating and averaged nonconvex projections
Here we show, in complete generality, that this method converges locally to a point in the intersection of the sets, at a linear rate governed by an associated regularity modulus
- Local Linear Convergence for Alternating and Averaged Nonconvex Projections
As a consequence, in the case of several arbitrary closed sets having linearly regular intersection at some point, the method of "averaged projections" converges locally at a linear rate to a point in the intersection Inexact versions of both algorithms also converge linearly
- Local Linear Convergence for Alternating and Averaged Nonconvex Projections
For this purpose, we use the Alternating Projections (AP) algorithm, which is a known efficient algorithm that finds a point of intersection of a collection of closed convex sets, and was
- Local convergence for alternating and averaged nonconvex . . .
In studying the convergence of iterative algorithms for nonconvex minimization problems or nonmonotone variational inequalities, we must content ourselves with a local theory
- Local Linear Convergence for Alternating and Averaged Nonconvex Projections
As a consequence, in the case of several arbitrary closed sets having strongly regular intersection at some point, the method of “averaged projections” converges locally at a linear rate to a point in the intersection Inexact versions of both algorithms also converge linearly
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