## An iterative procedure for obtaining I-projections onto the intersection of convex sets.(English)Zbl 0571.60006

A frequently occurring problem is to find a probability distribution lying within a set E which minimizes the I-divergence between it and a given distribution R. This is referred to as the I-projection of R onto E. I. Csiszar [ibid. 3, 146-158 (1975; Zbl 0318.60013)] has shown that when $$E=\cap^ t_ 1E_ i$$ is a finite intersection of closed, linear sets, a cyclic, iterative procedure which projects onto the individual $$E_ i$$ must converge to the desired I-projection on E, provided the sample space is finite.
Here we propose an iterative procedure, which requires only that the $$E_ i$$ be convex (and not necessarily linear), which under general conditions will converge to the desired I-projection of R onto $$\cap^ t_ i$$ $$E_ i$$.

### MSC:

 60A99 Foundations of probability theory 90C99 Mathematical programming 94A17 Measures of information, entropy 49M99 Numerical methods in optimal control

Zbl 0318.60013
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