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Proximal Point Methods in Metric Spaces

In: Numerical Optimization with Computational Errors

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  • Alexander J. Zaslavski

    (The Technion – Israel Institute of Technology)

Abstract

In this chapter 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 [55].

Suggested Citation

  • Alexander J. Zaslavski, 2016. "Proximal Point Methods in Metric Spaces," Springer Optimization and Its Applications, in: Numerical Optimization with Computational Errors, chapter 0, pages 149-168, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-30921-7_10
    DOI: 10.1007/978-3-319-30921-7_10
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