Error Sensitivity for Strongly Convergent Modifications of the Proximal Point Algorithm

Yamin Wang (), Fenghui Wang () and Hong-Kun Xu ()
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Yamin Wang: Henan Normal University
Fenghui Wang: Luoyang Normal University
Hong-Kun Xu: Hangzhou Dianzi University

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 3, No 10, 916 pages

Abstract: Abstract The proximal point algorithm plays an important role in finding zeros of maximal monotone operators. It has however only weak convergence in the infinite-dimensional setting. In the present paper, we provide two contraction-proximal point algorithms. The strong convergence of the two algorithms is proved under two different accuracy criteria on the errors. A new technique of argument is used, and this makes sure that our conditions, which are sufficient for the strong convergence of the algorithms, are weaker than those used by several other authors.

Keywords: Proximal point algorithm; Contraction-proximal point algorithm; Maximal monotone operator; Resolvent; Strong convergence; 47H05; 47J25; 65K15; 90C25 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-015-0835-4

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