The problem considered in this paper is that of finding a point which is common to almost all the members of a measurable family of closed convex subsets of Rn++, provided that such a point exists. The main results show that this problem can be solved by an iterative method essentially based on averaging at each step the Bregman projections with respect to f(x) = ∑ni=1 xi · ln xithe current iterate onto the given sets.
Bibliographical noteFunding Information:
The work of Y. Censor was partially supported by the grant HL-28438 at the Medical Image Processing Group (MIPG), Department of Radiology, the University of Pennsylvania, Philadelphia, PA, USA. The work of S. Reich was partially supported by the Fund for the Promotion of Research at the Technion and by the M. and M.L. Bank Mathematics Research Fund at the Technion. The authors are grateful to the referees for their suggestions.
- Bregman projection
- Entropic projection
- Modulus of local convexity
- Stochastic convex feasibility problem
- Very convex function
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics
- Applied Mathematics