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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.
MSC:
65J15Equations with nonlinear operators (numerical methods)
47J25Iterative procedures (nonlinear operator equations)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
References:
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