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Journals / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 1

The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces

Mohsen TAHERNİA
Sirous MORADİ
Somayeh JAFARİ
Pages
399–408
Publication Date
2020-02-06
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Afterwards, we prove that, under suitable conditions, the proposed algorithm converges strongly to the metric projection of some point onto the zero set of the involving maximal monotone operator.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we consider a proximal point algorithm for finding zeros of maximal monotone operators in complete CAT(0) spaces.
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Key Findings & Data:First, a necessary and sufficient condition is presented for the zero set of the operator to be nonempty.
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Conclusion & Impact:Afterwards, we prove that, under suitable conditions, the proposed algorithm converges strongly to the metric projection of some point onto the zero set of the involving maximal monotone operator.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Maximal monotone operator · proximal point algorithm · Hadamard space

Abstract

In this paper, we consider a proximal point algorithm for finding zeros of maximal monotone operators in complete CAT(0) spaces. First, a necessary and sufficient condition is presented for the zero set of the operator to be nonempty. Afterwards, we prove that, under suitable conditions, the proposed algorithm converges strongly to the metric projection of some point onto the zero set of the involving maximal monotone operator.

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Cite This Article

TAHERNİA, M., MORADİ, S., JAFARİ, S. (2020). The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 399–408. https://ajindex.com/articles/669322

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