A parallel hybrid bregman subgradient extragradient method for a system of pseudomonotone equilibrium and fixed point problems

Annel Thembinkosi Bokodisa; Lateef Olakunle Jolaoso; Maggie Aphane

doi:10.3390/sym13020216

A parallel hybrid bregman subgradient extragradient method for a system of pseudomonotone equilibrium and fixed point problems

Annel Thembinkosi Bokodisa, Lateef Olakunle Jolaoso^*, Maggie Aphane

^*Corresponding author for this work

Mathematics and Applied Mathematics

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

4 Citations (Scopus)

Abstract

We introduce a new parallel hybrid subgradient extragradient method for solving the system of the pseudomonotone equilibrium problem and common fixed point problem in real reflexive Banach spaces. The algorithm is designed such that its convergence does not require prior estimation of the Lipschitz-like constants of the finite bifunctions underlying the equilibrium problems. Moreover, a strong convergence result is proven without imposing strong conditions on the control sequences. We further provide some numerical experiments to illustrate the performance of the proposed algorithm and compare with some existing methods.

Original language	English
Article number	216
Pages (from-to)	1-24
Number of pages	24
Journal	Symmetry
Volume	13
Issue number	2
DOIs	https://doi.org/10.3390/sym13020216
Publication status	Published - Feb 2021

Keywords

Bregman distance
Bregman nonexpansive mappings
Equilibrium problem
Fixed point problem
Pseudomonotone
Real reflexive Banach spaces

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10.3390/sym13020216

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title = "A parallel hybrid bregman subgradient extragradient method for a system of pseudomonotone equilibrium and fixed point problems",

abstract = "We introduce a new parallel hybrid subgradient extragradient method for solving the system of the pseudomonotone equilibrium problem and common fixed point problem in real reflexive Banach spaces. The algorithm is designed such that its convergence does not require prior estimation of the Lipschitz-like constants of the finite bifunctions underlying the equilibrium problems. Moreover, a strong convergence result is proven without imposing strong conditions on the control sequences. We further provide some numerical experiments to illustrate the performance of the proposed algorithm and compare with some existing methods.",

keywords = "Bregman distance, Bregman nonexpansive mappings, Equilibrium problem, Fixed point problem, Pseudomonotone, Real reflexive Banach spaces",

author = "Bokodisa, {Annel Thembinkosi} and Jolaoso, {Lateef Olakunle} and Maggie Aphane",

note = "Publisher Copyright: {\textcopyright} 2021 by the authors. Li-censee MDPI, Basel, Switzerland.",

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language = "English",

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AU - Bokodisa, Annel Thembinkosi

AU - Jolaoso, Lateef Olakunle

AU - Aphane, Maggie

PY - 2021/2

Y1 - 2021/2

N2 - We introduce a new parallel hybrid subgradient extragradient method for solving the system of the pseudomonotone equilibrium problem and common fixed point problem in real reflexive Banach spaces. The algorithm is designed such that its convergence does not require prior estimation of the Lipschitz-like constants of the finite bifunctions underlying the equilibrium problems. Moreover, a strong convergence result is proven without imposing strong conditions on the control sequences. We further provide some numerical experiments to illustrate the performance of the proposed algorithm and compare with some existing methods.

AB - We introduce a new parallel hybrid subgradient extragradient method for solving the system of the pseudomonotone equilibrium problem and common fixed point problem in real reflexive Banach spaces. The algorithm is designed such that its convergence does not require prior estimation of the Lipschitz-like constants of the finite bifunctions underlying the equilibrium problems. Moreover, a strong convergence result is proven without imposing strong conditions on the control sequences. We further provide some numerical experiments to illustrate the performance of the proposed algorithm and compare with some existing methods.

KW - Bregman distance

KW - Bregman nonexpansive mappings

KW - Equilibrium problem

KW - Fixed point problem

KW - Pseudomonotone

KW - Real reflexive Banach spaces

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DO - 10.3390/sym13020216

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JO - Symmetry

JF - Symmetry

IS - 2

M1 - 216

ER -

A parallel hybrid bregman subgradient extragradient method for a system of pseudomonotone equilibrium and fixed point problems

Abstract

Keywords

UN SDGs

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