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Maximal Monotone Operators and the Proximal Point Algorithm in the Presence of Computational Errors

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Abstract

In a finite-dimensional Euclidean space, we study the convergence of a proximal point method to a solution of the inclusion induced by a maximal monotone operator, under the presence of computational errors. Most results known in the literature establish the convergence of proximal point methods, when computational errors are summable. In the present paper, the convergence of the method is established for nonsummable computational errors. We show that the proximal point method generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant.

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Authors and Affiliations

  1. Department of Mathematics, Technion, Haifa, Israel

    A. J. Zaslavski

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  1. A. J. Zaslavski
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Correspondence to A. J. Zaslavski.

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Communicated by V.F. Demyanov.

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Zaslavski, A.J. Maximal Monotone Operators and the Proximal Point Algorithm in the Presence of Computational Errors. J Optim Theory Appl 150, 20–32 (2011). https://doi.org/10.1007/s10957-011-9820-8

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  • DOI: https://doi.org/10.1007/s10957-011-9820-8

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