MODIFIED INERTIAL ALGORITHM FOR SOLVING MIXED EQUILIBRIUM PROBLEMS IN HADAMARD SPACES

Abdul Rahim Khan; Chinedu Izuchukwu; Maggie Aphane; Godwin Chidi Ugwunnadi

doi:10.3934/naco.2021039

MODIFIED INERTIAL ALGORITHM FOR SOLVING MIXED EQUILIBRIUM PROBLEMS IN HADAMARD SPACES

Abdul Rahim Khan
, Chinedu Izuchukwu
, Maggie Aphane
, Godwin Chidi Ugwunnadi^*

^*Corresponding author for this work

Department of Mathematics

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

2 Scopus citations

Abstract

The main purpose of this paper is to introduce the concept of modified inertial algorithm in Hadamard spaces. We emphasize that, as far as we know, this is the first time that this concept is being considered in this setting. Under some weak assumptions, we prove that the modified inertial algorithm converges strongly to a common solution of a finite family of mixed equilibrium problems and fixed point problem of a nonexpansive mapping. We also give a primary numerical illustration in the framework of Hadamard spaces, to show the efficiency of the modified inertial term in our proposed algorithm.

Original language	English
Pages (from-to)	859-877
Number of pages	19
Journal	Numerical Algebra, Control and Optimization
Volume	12
Issue number	4
DOIs	https://doi.org/10.3934/naco.2021039
State	Published - Dec 2022

Bibliographical note

Publisher Copyright:
© 2022, American Institute of Mathematical Sciences. All rights reserved.

Keywords

Hadamard space
Inertial algorithm
Mixed equilibrium problem
convex function
minimization problem
monotone bifunction

ASJC Scopus subject areas

Algebra and Number Theory
Control and Optimization
Applied Mathematics

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10.3934/naco.2021039

Cite this

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title = "MODIFIED INERTIAL ALGORITHM FOR SOLVING MIXED EQUILIBRIUM PROBLEMS IN HADAMARD SPACES",

abstract = "The main purpose of this paper is to introduce the concept of modified inertial algorithm in Hadamard spaces. We emphasize that, as far as we know, this is the first time that this concept is being considered in this setting. Under some weak assumptions, we prove that the modified inertial algorithm converges strongly to a common solution of a finite family of mixed equilibrium problems and fixed point problem of a nonexpansive mapping. We also give a primary numerical illustration in the framework of Hadamard spaces, to show the efficiency of the modified inertial term in our proposed algorithm.",

keywords = "Hadamard space, Inertial algorithm, Mixed equilibrium problem, convex function, minimization problem, monotone bifunction",

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year = "2022",

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AU - Izuchukwu, Chinedu

AU - Aphane, Maggie

AU - Ugwunnadi, Godwin Chidi

PY - 2022/12

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N2 - The main purpose of this paper is to introduce the concept of modified inertial algorithm in Hadamard spaces. We emphasize that, as far as we know, this is the first time that this concept is being considered in this setting. Under some weak assumptions, we prove that the modified inertial algorithm converges strongly to a common solution of a finite family of mixed equilibrium problems and fixed point problem of a nonexpansive mapping. We also give a primary numerical illustration in the framework of Hadamard spaces, to show the efficiency of the modified inertial term in our proposed algorithm.

AB - The main purpose of this paper is to introduce the concept of modified inertial algorithm in Hadamard spaces. We emphasize that, as far as we know, this is the first time that this concept is being considered in this setting. Under some weak assumptions, we prove that the modified inertial algorithm converges strongly to a common solution of a finite family of mixed equilibrium problems and fixed point problem of a nonexpansive mapping. We also give a primary numerical illustration in the framework of Hadamard spaces, to show the efficiency of the modified inertial term in our proposed algorithm.

KW - Hadamard space

KW - Inertial algorithm

KW - Mixed equilibrium problem

KW - convex function

KW - minimization problem

KW - monotone bifunction

UR - https://www.scopus.com/pages/publications/85141732103

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M3 - Article

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VL - 12

SP - 859

EP - 877

JO - Numerical Algebra, Control and Optimization

JF - Numerical Algebra, Control and Optimization

IS - 4

ER -

MODIFIED INERTIAL ALGORITHM FOR SOLVING MIXED EQUILIBRIUM PROBLEMS IN HADAMARD SPACES

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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