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The expected-projection method: Its behavior and applications to linear operator equations and convex optimization. (English) Zbl 0860.90108

Summary: It was shown by the author and S. D. Flåm [Numer. Funct. Anal. Optimization 16, No. 5-6, 601-636 (1995; Zbl 0834.65041)] that, under some conditions, sequences generated by the expected projection method (EPM) in Hilbert spaces approximate almost common points of measurable families of closed convex subsets provided that such points exist. In this work, we study the behavior of the EPM in the more general situation when the involved sets may or may not have almost common points and we give necessary and sufficient conditions for weak and strong convergence. Also, we show how the EPM can be applied to finding solutions of linear operator equations and to solving convex optimization problems.

MSC:

90C30 Nonlinear programming
45B05 Fredholm integral equations

Citations:

Zbl 0834.65041
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