ON THE PROXIMAL POINT ALGORITHM OF HYBRID-TYPE IN FLAT HADAMARD SPACES WITH APPLICATIONS

Lawal Yusuf Haruna; Godwin Chidi Ugwunnadi; Bashir Ali

doi:10.46793/KgJMat2406.845H

ON THE PROXIMAL POINT ALGORITHM OF HYBRID-TYPE IN FLAT HADAMARD SPACES WITH APPLICATIONS

Lawal Yusuf Haruna
, Godwin Chidi Ugwunnadi
, Bashir Ali

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we introduce a hybrid-type proximal point algorithm for approximating zero of monotone operator in Hadamard-type spaces. We then prove that a sequence generated by the algorithm involving Mann-type iteration converges strongly to a zero of the said operator in the setting of flat Hadamard spaces. To the best of our knowledge, this result presents the first hybrid-type proximal point algorithm in the space. The result is applied to convex minimization and fixed point problems.

Original language	English
Pages (from-to)	845-857
Number of pages	13
Journal	Kragujevac Journal of Mathematics
Volume	48
Issue number	6
DOIs	https://doi.org/10.46793/KgJMat2406.845H
Publication status	Published - 2024
Externally published	Yes

Keywords

Fixed Points
flat Hadamard spaces
hybrid-type algorithm
monotone operators
proximal point algorithm

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10.46793/KgJMat2406.845H

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abstract = "In this paper, we introduce a hybrid-type proximal point algorithm for approximating zero of monotone operator in Hadamard-type spaces. We then prove that a sequence generated by the algorithm involving Mann-type iteration converges strongly to a zero of the said operator in the setting of flat Hadamard spaces. To the best of our knowledge, this result presents the first hybrid-type proximal point algorithm in the space. The result is applied to convex minimization and fixed point problems.",

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language = "English",

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AU - Ali, Bashir

PY - 2024

Y1 - 2024

N2 - In this paper, we introduce a hybrid-type proximal point algorithm for approximating zero of monotone operator in Hadamard-type spaces. We then prove that a sequence generated by the algorithm involving Mann-type iteration converges strongly to a zero of the said operator in the setting of flat Hadamard spaces. To the best of our knowledge, this result presents the first hybrid-type proximal point algorithm in the space. The result is applied to convex minimization and fixed point problems.

AB - In this paper, we introduce a hybrid-type proximal point algorithm for approximating zero of monotone operator in Hadamard-type spaces. We then prove that a sequence generated by the algorithm involving Mann-type iteration converges strongly to a zero of the said operator in the setting of flat Hadamard spaces. To the best of our knowledge, this result presents the first hybrid-type proximal point algorithm in the space. The result is applied to convex minimization and fixed point problems.

KW - Fixed Points

KW - flat Hadamard spaces

KW - hybrid-type algorithm

KW - monotone operators

KW - proximal point algorithm

UR - https://www.scopus.com/pages/publications/85212428354

U2 - 10.46793/KgJMat2406.845H

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JF - Kragujevac Journal of Mathematics

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ER -

ON THE PROXIMAL POINT ALGORITHM OF HYBRID-TYPE IN FLAT HADAMARD SPACES WITH APPLICATIONS

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Keywords

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