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Zbl 1082.65058
Bauschke, Heinz H.; Combettes, Patrick L.
A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces. (English)
[J] Math. Oper. Res. 26, No. 2, 248-264 (2001). ISSN 1526-5471; ISSN 0364-765X/e

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 2000:: *65J15 Equations with nonlinear operators (numerical methods)
47J25 Methods for solving nonlinear operator equations (general)
90C48 Programming in abstract spaces

Keywords: Convex feasibility, Fejér-monotonicity, firmly nonexpansive mapping, fixed point, Haugazeau, maximal monotone operator, projection, proximal point algorithm, resolvent, subgradient algorithm.

Cited in: Zbl 1232.49017 Zbl 1222.47094

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