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A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces. (English) Zbl 1082.65058
Summary: We consider a wide class of iterative methods arising in numerical mathematics and optimization that are known to converge only weakly. Exploiting an idea originally proposed by Haugazeau, we present a simple modification of these methods that makes them strongly convergent without additional assumptions. Several applications are discussed.

MSC:
65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
90C48 Programming in abstract spaces
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