ON LOCAL CONVERGENCE OF THE METHOD OF ALTERNATING PROJECTIONS

Dominikus Noll (1) , Aude Rondepierre (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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, ∞).

Mots clés: Alternating projections; local convergence; subanalytic set; separable intersection; tangential intersection; Hölder regularity; Gerchberg-Saxton error reduction

Domaines: Optimisation et contrôle [math.OC]

Dominikus Noll, Aude Rondepierre. ON LOCAL CONVERGENCE OF THE METHOD OF ALTERNATING PROJECTIONS. Foundations of Computational Mathematics, 2016, 16 (2), pp 425-455. ⟨hal-01807098⟩