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Generalized Bregman Projections in Convex Feasibility Problems

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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.

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  1. Systems Research Institute, Warsaw, Poland

    K. C. Kiwiel (Professor)

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  1. K. C. Kiwiel
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Kiwiel, K.C. Generalized Bregman Projections in Convex Feasibility Problems. Journal of Optimization Theory and Applications 96, 139–157 (1998). https://doi.org/10.1023/A:1022619318462

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