Butnariu, D. The expected-projection method: Its behavior and applications to linear operator equations and convex optimization. (English) Zbl 0860.90108 J. Appl. Anal. 1, No. 1, 93-108 (1995). 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. Cited in 5 Documents MSC: 90C30 Nonlinear programming 45B05 Fredholm integral equations Keywords:Bochner integral; asymptotic center of sequence; stochastic convex feasibility problem; expected projection method; Hilbert spaces; necessary and sufficient conditions for weak and strong convergence; linear operator equations Citations:Zbl 0834.65041 PDFBibTeX XMLCite \textit{D. Butnariu}, J. Appl. Anal. 1, No. 1, 93--108 (1995; Zbl 0860.90108) Full Text: DOI EuDML