Two accelerated double inertial algorithms for variational inequalities on Hadamard manifolds

Bing Tan; Hammed Anuoluwapo Abass; Songxiao Li; Olawale Kazeem Oyewole

doi:10.1016/j.cnsns.2025.108734

Two accelerated double inertial algorithms for variational inequalities on Hadamard manifolds

Bing Tan, Hammed Anuoluwapo Abass^*, Songxiao Li, Olawale Kazeem Oyewole

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

Two modified double inertial proximal point algorithms are proposed for solving variational inequality problems with a pseudomonotone vector field in the settings of a Hadamard manifold. Weak convergence of the proposed methods is attained without the requirement of Lipschitz continuity conditions. The convergence efficiency of the proposed algorithms is improved with the help of the double inertial technique and the non-monotonic self-adaptive step size rule. We present a numerical experiment to demonstrate the effectiveness of the proposed algorithm compared to several existing ones. The results extend and generalize many recent methods in the literature.

Original language	English
Article number	108734
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	145
DOIs	https://doi.org/10.1016/j.cnsns.2025.108734
Publication status	Published - Jun 2025
Externally published	Yes

Keywords

Double inertial
Hadamard manifold
Proximal point algorithm
Uniformly continuous
Variational inequality problem

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10.1016/j.cnsns.2025.108734

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title = "Two accelerated double inertial algorithms for variational inequalities on Hadamard manifolds",

abstract = "Two modified double inertial proximal point algorithms are proposed for solving variational inequality problems with a pseudomonotone vector field in the settings of a Hadamard manifold. Weak convergence of the proposed methods is attained without the requirement of Lipschitz continuity conditions. The convergence efficiency of the proposed algorithms is improved with the help of the double inertial technique and the non-monotonic self-adaptive step size rule. We present a numerical experiment to demonstrate the effectiveness of the proposed algorithm compared to several existing ones. The results extend and generalize many recent methods in the literature.",

keywords = "Double inertial, Hadamard manifold, Proximal point algorithm, Uniformly continuous, Variational inequality problem",

author = "Bing Tan and Abass, \{Hammed Anuoluwapo\} and Songxiao Li and Oyewole, \{Olawale Kazeem\}",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier B.V.",

year = "2025",

month = jun,

doi = "10.1016/j.cnsns.2025.108734",

language = "English",

volume = "145",

journal = "Communications in Nonlinear Science and Numerical Simulation",

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TY - JOUR

T1 - Two accelerated double inertial algorithms for variational inequalities on Hadamard manifolds

AU - Tan, Bing

AU - Abass, Hammed Anuoluwapo

AU - Li, Songxiao

AU - Oyewole, Olawale Kazeem

PY - 2025/6

Y1 - 2025/6

N2 - Two modified double inertial proximal point algorithms are proposed for solving variational inequality problems with a pseudomonotone vector field in the settings of a Hadamard manifold. Weak convergence of the proposed methods is attained without the requirement of Lipschitz continuity conditions. The convergence efficiency of the proposed algorithms is improved with the help of the double inertial technique and the non-monotonic self-adaptive step size rule. We present a numerical experiment to demonstrate the effectiveness of the proposed algorithm compared to several existing ones. The results extend and generalize many recent methods in the literature.

AB - Two modified double inertial proximal point algorithms are proposed for solving variational inequality problems with a pseudomonotone vector field in the settings of a Hadamard manifold. Weak convergence of the proposed methods is attained without the requirement of Lipschitz continuity conditions. The convergence efficiency of the proposed algorithms is improved with the help of the double inertial technique and the non-monotonic self-adaptive step size rule. We present a numerical experiment to demonstrate the effectiveness of the proposed algorithm compared to several existing ones. The results extend and generalize many recent methods in the literature.

KW - Double inertial

KW - Hadamard manifold

KW - Proximal point algorithm

KW - Uniformly continuous

KW - Variational inequality problem

UR - http://www.scopus.com/inward/record.url?scp=86000717198&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2025.108734

DO - 10.1016/j.cnsns.2025.108734

M3 - Article

AN - SCOPUS:86000717198

SN - 1007-5704

VL - 145

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 108734

ER -

Two accelerated double inertial algorithms for variational inequalities on Hadamard manifolds

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Keywords

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