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On convergence of the proximal point algorithm in Banach spaces


Authors: Shin-ya Matsushita and Li Xu
Journal: Proc. Amer. Math. Soc. 139 (2011), 4087-4095
MSC (2010): Primary 65K10, 90C25; Secondary 47J25, 47H05, 47H04
DOI: https://doi.org/10.1090/S0002-9939-2011-10883-9
Published electronically: March 25, 2011
MathSciNet review: 2823053
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we give a sufficient condition which guarantees that the sequence generated by the proximal point algorithm terminates after a finite number of iterations.


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Additional Information

Shin-ya Matsushita
Affiliation: Department of Electronics and Information Systems, Faculty of Systems Sciences and Technology, Akita Prefectural University, 84-4 Ebinokuchi Tsuchiya, Yurihonjo City, Akita, 015-0055 Japan
Email: matsushita@akita-pu.ac.jp

Li Xu
Affiliation: Department of Electronics and Information Systems, Faculty of Systems Sciences and Technology, Akita Prefectural University, 84-4 Ebinokuchi Tsuchiya, Yurihonjo City, Akita, 015-0055 Japan
Email: xuli@akita-pu.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-2011-10883-9
Keywords: Proximal point algorithm, finite termination of algorithm, maximal monotone operator, paramonotone operator, Banach space, weak sharp minima.
Received by editor(s): September 6, 2010
Published electronically: March 25, 2011
Additional Notes: The first author was supported by Grant-in-Aid for Young Scientists (B) No. 20740084, the Ministry of Education, Culture, Sports, Science and Technology, Japan
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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