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Convergence of Bregman Projection Methods for Solving Consistent Convex Feasibility Problems in Reflexive Banach Spaces

Author

Listed:
  • Y. Alber

    (Technion-Israel Institute of Technology)

  • D. Butnariu

    (Technion-Israel Institute of Technology)

Abstract

The problem that we consider is whether or under what conditions sequences generated in reflexive Banach spaces by cyclic Bregman projections on finitely many closed convex subsets Q i with nonempty intersection converge to common points of the given sets.

Suggested Citation

  • Y. Alber & D. Butnariu, 1997. "Convergence of Bregman Projection Methods for Solving Consistent Convex Feasibility Problems in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 92(1), pages 33-61, January.
    • Handle: RePEc:spr:joptap:v:92:y:1997:i:1:d:10.1023_a:1022631928592
    DOI: 10.1023/A:1022631928592
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    Cited by:

    1. Fischer, Aurélie, 2010. "Quantization and clustering with Bregman divergences," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2207-2221, October.
    2. Juan Enrique Martínez-Legaz & Maryam Tamadoni Jahromi & Eskandar Naraghirad, 2022. "On Bregman-Type Distances and Their Associated Projection Mappings," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 107-117, June.
    3. M. B. Lee & S. H. Park, 2004. "Convergence of Sequential Parafirmly Nonexpansive Mappings in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 549-571, December.
    4. Gaurav Mittal & Ankik Kumar Giri, 2022. "Novel Multi-level Projected Iteration to Solve Inverse Problems with Nearly Optimal Accuracy," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 643-680, August.

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