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Legendre functions and the method of random Bregman projections. (English) Zbl 0894.49019
The authors consider in Euclidean spaces the convex feasibility problem:
Given closed convex intersection sets $$C_1,\dots, C_N$$, find a point in $$C_1\cap\cdots\cap C_N$$ within the framework of Convex Analysis.
New insights are obtained and the rich class of Bregman/Legendre functions is introduced. Special attention is given to examples, some of which connect to Pythagorean means and to Convex Analysis on the Hermitian or symmetric matrices.

##### MSC:
 90C25 Convex programming
##### Keywords:
convex feasibility problem; Bregman/Legendre functions
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