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The perturbed Tikhonov’s algorithm and some of its applications. (English) Zbl 0821.65036

The author considers the problem of finding a zero of a nonlinear monotone operator (in the sense of Minty and Browder) in a real Hilbert space. The operator may be given approximately with an error tending to zero along the sequence of approximations. For solving the problem an algorithm based on the concept of Tikhonov’s regularization is proposed. Results of numerical tests with model finite-dimensional optimization problems are presented.
Note of the reviewer: The results of the theoretical part of the work are not new. A detailed analysis of Tikhonov’s regularization of nonlinear monotone operator equations was given by F. E. Browder, Ya. I. Al’ber, F. P. Vasil’ev, A. B. Bakushinsky in the sixties-eighties. There are no references to these authors’ works in the paper.

MSC:

65J15 Numerical solutions to equations with nonlinear operators
47H05 Monotone operators and generalizations
47J25 Iterative procedures involving nonlinear operators
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References:

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