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Convergence theorems for inertial KM-type algorithms. (English) Zbl 1156.65054
For the approximation of fixed points of nonlinear operators in a Hilbert space, a general method is studied that allows to unify iterations of Krasnoselskij-Mann-type with a relaxation or damping factor and inertial-type extrapolation methods. Results on the weak convergence are shown. Applications are given for constraint minimization problems, subgradient projection methods, and problems with maximal monotone operator.

65J15Equations with nonlinear operators (numerical methods)
47J25Iterative procedures (nonlinear operator equations)
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
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