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arXiv · 1304.7078

Asymptotic behavior of compositions of under-relaxed nonexpansive operators

J. -B. Baillon·P. L. Combettes·R. Cominetti
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Abstract

In general there exists no relationship between the fixed point sets of the composition and of the average of a family of nonexpansive operators in Hilbert spaces. In this paper, we establish an asymptotic principle connecting the cycles generated by under-relaxed compositions of nonexpansive operators to the fixed points of the average of these operators. In the special case when the operators are projectors onto closed convex sets, we prove a conjecture by De Pierro which has so far been established only for projections onto affine subspaces.

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J. -B. Baillon, P. L. Combettes, R. Cominetti. 2013-04-26. Asymptotic behavior of compositions of under-relaxed nonexpansive operators. https://arxiv.org/abs/1304.7078

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