Abstract
The problem considered in this paper is that of finding a point which iscommon to almost all the members of a measurable family of closed convexsubsets of R++ n, provided that such a point exists.The main results show that this problem can be solved by an iterative methodessentially based on averaging at each step the Bregman projections withrespect to f(x)=∑i=1 nxi· ln xi ofthe current iterate onto the given sets.
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Butnariu, D., Censor, Y. & Reich, S. Iterative Averaging of Entropic Projections for Solving Stochastic Convex Feasibility Problems. Computational Optimization and Applications 8, 21–39 (1997). https://doi.org/10.1023/A:1008654413997
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DOI: https://doi.org/10.1023/A:1008654413997