Year 2020, Volume 49 , Issue 1, Pages 399 - 408 2020-02-06

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

Mohsen TAHERNİA [1] , Sirous MORADİ [2] , Somayeh JAFARİ [3]


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.
Maximal monotone operator, proximal point algorithm, Hadamard space, nonexpansive mapping, resolvent operator
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0002-0014-1052
Author: Mohsen TAHERNİA
Institution: Arak University
Country: Iran


Orcid: 0000-0002-8640-7252
Author: Sirous MORADİ (Primary Author)
Institution: Arak University
Country: Iran


Orcid: 0000-0002-3832-3177
Author: Somayeh JAFARİ
Institution: Arak University
Country: Iran


Dates

Publication Date : February 6, 2020

Bibtex @research article { hujms470975, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {399 - 408}, doi = {10.15672/hujms.470975}, title = {The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces}, key = {cite}, author = {TAHERNİA, Mohsen and MORADİ, Sirous and JAFARİ, Somayeh} }
APA 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 , 49 (1) , 399-408 . DOI: 10.15672/hujms.470975
MLA TAHERNİA, M , MORADİ, S , JAFARİ, S . "The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 399-408 <https://dergipark.org.tr/en/pub/hujms/issue/52287/470975>
Chicago TAHERNİA, M , MORADİ, S , JAFARİ, S . "The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 399-408
RIS TY - JOUR T1 - The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces AU - Mohsen TAHERNİA , Sirous MORADİ , Somayeh JAFARİ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.470975 DO - 10.15672/hujms.470975 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 399 EP - 408 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.470975 UR - https://doi.org/10.15672/hujms.470975 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces %A Mohsen TAHERNİA , Sirous MORADİ , Somayeh JAFARİ %T The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/hujms.470975 %U 10.15672/hujms.470975
ISNAD TAHERNİA, Mohsen , MORADİ, Sirous , JAFARİ, Somayeh . "The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 399-408 . https://doi.org/10.15672/hujms.470975
AMA TAHERNİA M , MORADİ S , JAFARİ S . The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 399-408.
Vancouver TAHERNİA M , MORADİ S , JAFARİ S . The strong convergence of a proximal point algorithm in complete CAT(0) metric spaces. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 408-399.