The modified proximal point algorithm in Hadamard spaces

The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (convergence in metric) to a minimizer of convex objective functions. The results extend sev...

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Bibliographic Details
Published in:Journal of inequalities and applications 2018, Vol.2018 (1), p.1-10, Article 124
Main Authors: Chang, Shih-sen, Wang, Lin, Wen, Ching-Feng, Zhang, Jian Qiang
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Applications of Mathematics
CAT $\operatorname{CAT}$ space
Convergence
Curvature
Hadamard space
Hilbert space
Implicit iterative rule
Mathematics
Mathematics and Statistics
Moreau–Yosida resolvent
Proximal point algorithm
Variational inequality
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Summary:The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (convergence in metric) to a minimizer of convex objective functions. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-018-1713-z