Proximal Point Subgradient Algorithm

Alexander J. Zaslavski
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Alexander J. Zaslavski: Technion - Israel Institute of Technology

Chapter Chapter 3 in Optimization on Solution Sets of Common Fixed Point Problems, 2021, pp 103-173 from Springer

Abstract: Abstract In this chapter we consider a minimization of a convex function on an intersection of two sets in a Hilbert space. One of them is a common fixed point set of a finite family of quasi-nonexpansive mappings while the second one is a common zero point set of finite family of maximal monotone operators. Our goal is to obtain a good approximate solution of the problem in the presence of computational errors. We use the Cimmino proximal point subgradient algorithm, the iterative proximal point subgradient algorithm and the dynamic string-averaging proximal point subgradient algorithm and show that each of them generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. Moreover, if we known computational errors for our algorithm, we find out what an approximate solution can be obtained and how many iterates one needs for this.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-78849-0_3

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DOI: 10.1007/978-3-030-78849-0_3

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