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On the Finite Convergence of a Projected Cutter Method

Author

Listed:
  • Heinz H. Bauschke

    (University of British Columbia)

  • Caifang Wang

    (Shanghai Maritime University)

  • Xianfu Wang

    (University of British Columbia)

  • Jia Xu

    (University of British Columbia)

Abstract

The subgradient projection iteration is a classical method for solving a convex inequality. Motivated by works of Polyak and of Crombez, we present and analyze a more general method for finding a fixed point of a cutter, provided that the fixed point set has nonempty interior. Our assumptions on the parameters are more general than existing ones. Various limiting examples and comparisons are provided.

Suggested Citation

  • Heinz H. Bauschke & Caifang Wang & Xianfu Wang & Jia Xu, 2015. "On the Finite Convergence of a Projected Cutter Method," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 901-916, June.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:3:d:10.1007_s10957-014-0659-7
    DOI: 10.1007/s10957-014-0659-7
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    References listed on IDEAS

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    1. H. H. Bauschke & S. G. Kruk, 2004. "Reflection-Projection Method for Convex Feasibility Problems with an Obtuse Cone," Journal of Optimization Theory and Applications, Springer, vol. 120(3), pages 503-531, March.
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    Cited by:

    1. Yair Censor & Daniel Reem & Maroun Zaknoon, 2022. "A generalized block-iterative projection method for the common fixed point problem induced by cutters," Journal of Global Optimization, Springer, vol. 84(4), pages 967-987, December.

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