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Generalized Bregman Projections in Convex Feasibility Problems

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  • K. C. Kiwiel

    (Systems Research Institute)

Abstract

We present a method for finding common points of finitely many closed convex sets in Euclidean space. The Bregman extension of the classical method of cyclic orthogonal projections employs nonorthogonal projections induced by a convex Bregman function, whereas the Bauschke and Borwein method uses Bregman/Legendre functions. Our method works with generalized Bregman functions (B-functions) and inexact projections, which are easier to compute than the exact ones employed in other methods. We also discuss subgradient algorithms with Bregman projections.

Suggested Citation

  • K. C. Kiwiel, 1998. "Generalized Bregman Projections in Convex Feasibility Problems," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 139-157, January.
    • Handle: RePEc:spr:joptap:v:96:y:1998:i:1:d:10.1023_a:1022619318462
    DOI: 10.1023/A:1022619318462
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    References listed on IDEAS

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    1. Jonathan Eckstein, 1993. "Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 202-226, February.
    2. Krzysztof C. Kiwiel, 1997. "Free-Steering Relaxation Methods for Problems with Strictly Convex Costs and Linear Constraints," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 326-349, May.
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