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arXiv · 2107.00365

Local linear convergence of alternating projections in metric spaces with bounded curvature

Adrian S. Lewis·Genaro López-Acedo·Adriana Nicolae
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Abstract

We consider the popular and classical method of alternating projections for finding a point in the intersection of two closed sets. By situating the algorithm in a metric space, equipped only with well-behaved geodesics and angles (in the sense of Alexandrov), we are able to highlight the two key geometric ingredients in a standard intuitive analysis of local linear convergence. The first is a transversality-like condition on the intersection; the second is a convexity-like condition on one set: "uniform approximation by geodesics."

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Adrian S. Lewis, Genaro López-Acedo, Adriana Nicolae. 2021-07-01. Local linear convergence of alternating projections in metric spaces with bounded curvature. https://doi.org/10.1137/21m1431576

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