A TECHNIQUE WITH DIMINISHING AND NON-SUMMABLE STEP-SIZE FOR MONOTONE INCLUSION PROBLEMS IN BANACH SPACES

Abubakar Adamu; Dilber Uzun Ozsahin; Abdulkarim Hassan Ibrahim; Pongsakorn Sunthrayuth

doi:10.22771/nfaa.2023.28.04.13

A TECHNIQUE WITH DIMINISHING AND NON-SUMMABLE STEP-SIZE FOR MONOTONE INCLUSION PROBLEMS IN BANACH SPACES

Abubakar Adamu, Dilber Uzun Ozsahin, Abdulkarim Hassan Ibrahim, Pongsakorn Sunthrayuth^*

^*Corresponding author for this work

Interdisciplinary Research Center for Smart Mobility and Logistics

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

2 Scopus citations

Abstract

In this paper, an algorithm for approximating zeros of sum of three monotone operators is introduced and its convergence properties are studied in the setting of 2-uniformly convex and uniformly smooth Banach spaces. Unlike the existing algorithms whose step-sizes usually depend on the knowledge of the operator norm or Lipschitz constant, a nice feature of the proposed algorithm is the fact that it requires only a diminishing and non-summable step-size to obtain strong convergence of the iterates to a solution of the problem. Finally, the proposed algorithm is implemented in the setting of a classical Banach space to support the theory established.

Original language	English
Pages (from-to)	1051-1067
Number of pages	17
Journal	Nonlinear Functional Analysis and Applications
Volume	28
Issue number	4
DOIs	https://doi.org/10.22771/nfaa.2023.28.04.13
State	Published - 2023

Bibliographical note

Publisher Copyright:
© 2023 Kyungnam University Press

Keywords

Lipschitz
Monotone
convex minimization
zeros

ASJC Scopus subject areas

Analysis
Numerical Analysis
Control and Optimization
Applied Mathematics

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10.22771/nfaa.2023.28.04.13

Cite this

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title = "A TECHNIQUE WITH DIMINISHING AND NON-SUMMABLE STEP-SIZE FOR MONOTONE INCLUSION PROBLEMS IN BANACH SPACES",

abstract = "In this paper, an algorithm for approximating zeros of sum of three monotone operators is introduced and its convergence properties are studied in the setting of 2-uniformly convex and uniformly smooth Banach spaces. Unlike the existing algorithms whose step-sizes usually depend on the knowledge of the operator norm or Lipschitz constant, a nice feature of the proposed algorithm is the fact that it requires only a diminishing and non-summable step-size to obtain strong convergence of the iterates to a solution of the problem. Finally, the proposed algorithm is implemented in the setting of a classical Banach space to support the theory established.",

keywords = "Lipschitz, Monotone, convex minimization, zeros",

author = "Abubakar Adamu and Ozsahin, \{Dilber Uzun\} and Ibrahim, \{Abdulkarim Hassan\} and Pongsakorn Sunthrayuth",

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doi = "10.22771/nfaa.2023.28.04.13",

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T1 - A TECHNIQUE WITH DIMINISHING AND NON-SUMMABLE STEP-SIZE FOR MONOTONE INCLUSION PROBLEMS IN BANACH SPACES

AU - Adamu, Abubakar

AU - Ozsahin, Dilber Uzun

AU - Ibrahim, Abdulkarim Hassan

AU - Sunthrayuth, Pongsakorn

PY - 2023

Y1 - 2023

N2 - In this paper, an algorithm for approximating zeros of sum of three monotone operators is introduced and its convergence properties are studied in the setting of 2-uniformly convex and uniformly smooth Banach spaces. Unlike the existing algorithms whose step-sizes usually depend on the knowledge of the operator norm or Lipschitz constant, a nice feature of the proposed algorithm is the fact that it requires only a diminishing and non-summable step-size to obtain strong convergence of the iterates to a solution of the problem. Finally, the proposed algorithm is implemented in the setting of a classical Banach space to support the theory established.

AB - In this paper, an algorithm for approximating zeros of sum of three monotone operators is introduced and its convergence properties are studied in the setting of 2-uniformly convex and uniformly smooth Banach spaces. Unlike the existing algorithms whose step-sizes usually depend on the knowledge of the operator norm or Lipschitz constant, a nice feature of the proposed algorithm is the fact that it requires only a diminishing and non-summable step-size to obtain strong convergence of the iterates to a solution of the problem. Finally, the proposed algorithm is implemented in the setting of a classical Banach space to support the theory established.

KW - Lipschitz

KW - Monotone

KW - convex minimization

KW - zeros

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JO - Nonlinear Functional Analysis and Applications

JF - Nonlinear Functional Analysis and Applications

IS - 4

ER -

A TECHNIQUE WITH DIMINISHING AND NON-SUMMABLE STEP-SIZE FOR MONOTONE INCLUSION PROBLEMS IN BANACH SPACES

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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