A modified proximal point algorithm in geodesic metric space-Reference-Cited by-同舟云学术

A modified proximal point algorithm in geodesic metric space

Published:2023 Issue:2 Volume:8 Page:4304-4320
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Garodia Chanchal¹,Uddin Izhar¹,Abdalla Bahaaeldin²,Abdeljawad Thabet²³

Affiliation:

1. Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi-110025, India

2. Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia

3. Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Abstract

<abstract><p>Proximal point algorithm is one of the most popular technique to find either zero of monotone operator or minimizer of a lower semi-continuous function. In this paper, we propose a new modified proximal point algorithm for solving minimization problems and common fixed point problems in CAT(0) spaces. We prove $ \Delta $ and strong convergence of the proposed algorithm. Our results extend and improve the corresponding recent results in the literature.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference46 articles.

1. B. Martinet, Régularisation d'inéuations variationnelles par approximations successives, Rev. Fr. Inform. Rech. Oper., 4 (1970), 154–158.

2. R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 14 (1977), 877–898. https://doi.org/10.1137/0314056

3. H. Brézis, P. Lions, Produits infinis de résolvantes, Israel J. Math., 29 (1978), 329–345. https://doi.org/10.1007/BF02761171

4. O. Güler, On the convergence of the proximal point algorithm for convex minimization, SIAM J. Control Optim., 29 (1991), 403–419. https://doi.org/10.1137/0329022

5. S. Kamimura, W. Takahashi, Approximating solutions of maximal monotone operators in Hilbert spaces, J Approx. Theory, 106 (2000), 226–240. https://doi.org/10.1006/jath.2000.3493

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On Relational Weak Fℜm,η-Contractive Mappings and Their Applications;Symmetry;2023-04-15