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An acceleration scheme for Dykstra’s algorithm

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  • Williams López
  • Marcos Raydan

Abstract

Dykstra’s algorithm is an iterative alternating projection procedure for solving the best approximation problem: find the closest point, to a given one, in the intersection of a finite number of closed and convex sets. The main drawback of Dykstra’s algorithm is its frequent slow convergence. In this work we develop an acceleration scheme with a strong geometrical flavor, which guarantees termination at the solution in two cycles of projections in the case of two closed subspaces. The proposed scheme can also be applied to any other alternating projection algorithm that solves the best approximation problem. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Williams López & Marcos Raydan, 2016. "An acceleration scheme for Dykstra’s algorithm," Computational Optimization and Applications, Springer, vol. 63(1), pages 29-44, January.
    • Handle: RePEc:spr:coopap:v:63:y:2016:i:1:p:29-44
    DOI: 10.1007/s10589-015-9768-y
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    References listed on IDEAS

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    1. A. Cegielski & R. Dylewski, 2010. "Variable target value relaxed alternating projection method," Computational Optimization and Applications, Springer, vol. 47(3), pages 455-476, November.
    2. N. Echebest & M. Guardarucci & H. Scolnik & M. Vacchino, 2005. "An Accelerated Iterative Method with Diagonally Scaled Oblique Projections for Solving Linear Feasibility Problems," Annals of Operations Research, Springer, vol. 138(1), pages 235-257, September.
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    Cited by:

    1. Oumaima Benchettou & Abdeslem Hafid Bentbib & Abderrahman Bouhamidi, 2023. "An Accelerated Tensorial Double Proximal Gradient Method for Total Variation Regularization Problem," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 111-134, July.

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