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Inexact Proximal Point Methods in Metric Spaces

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Abstract

We study the local convergence of a proximal point method in a metric space under the presence of 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 some constant. The principle assumption is a local error bound condition which relates the growth of an objective function to the distance to the set of minimizers introduced by Hager and Zhang (SIAM J Control Optim 46:1683–1704, 2007).

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Authors and Affiliations

  1. Department of Mathematics, The Technion—Israel Institute of Technology, 32000, Haifa, Israel

    Alexander J. Zaslavski

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  1. Alexander J. Zaslavski
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Zaslavski, A.J. Inexact Proximal Point Methods in Metric Spaces. Set-Valued Anal 19, 589–608 (2011). https://doi.org/10.1007/s11228-011-0185-9

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  • DOI: https://doi.org/10.1007/s11228-011-0185-9

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