Variable metric quasi-Fejér monotonicity. (English) Zbl 1266.65087

Combettes, Patrick L.; Vũ, Băng C.

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 78, 17-31 (2013).

The authors generalize the context of quasi-Fejér monotonicity to variable metrics in Hilbert spaces for convergence analysis of various algorithms in applied nonlinear analysis. Both weak and strong convergence are established while the underlying norm may vary at each iteration. Applications to convex feasibility and inverse problems are discussed and illustrated with examples.

Reviewer: Zhen Mei (Toronto)

MSC:

65J15	Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
90C25	Convex programming
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

convex feasibility problem; inverse problem; quasi-Fejér monotonicity; variable metric; Hilbert space