Proximal Point Method in Hilbert Spaces

Alexander J. Zaslavski
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Alexander J. Zaslavski: The Technion – Israel Institute of Technology

Chapter Chapter 9 in Numerical Optimization with Computational Errors, 2016, pp 137-147 from Springer

Abstract: Abstract In this chapter we study the convergence of a proximal point method under the presence of computational errors. Most results known in the literature show the convergence of proximal point methods when computational errors are summable. In this chapter 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 some constant.

Keywords: Proximal Point Method; Hilbert Space; Computational Errors; Good Approximate Solution; Lower Semicontinuous Convex Function (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-30921-7_9

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DOI: 10.1007/978-3-319-30921-7_9

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