Modified inertial subgradient extragradient method for equilibrium problems
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Lateef Olakunle Jolaoso
and
Regina N. Nwokoye
Abstract
The subgradient extragradient method with inertial extrapolation step x n + θ n (x n − x n−1) (also known as inertial subgradient extragradient method) has been studied extensively in the literature for solving variational inequalities and equilibrium problems. Most of the inertial subgradient extragradient methods in the literature for both variational inequalities and equilibrium problems have not considered the special case when the inertial factor θ n = 1. The convergence results have always been obtained when the inertial factor θ n is assumed 0 ≤ θ n < 1. This paper considers the relaxed inertial version of subgradient extragradient method for equilibrium problems with 0 ≤ θ n ≤ 1. We give both weak and strong convergence results using this inertial subgradient extragradient method and also give some numerical illustrations.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Numerical solutions for variable-order fractional Gross–Pitaevskii equation with two spectral collocation approaches
- Threshold dynamics of an HIV-1 model with both virus-to-cell and cell-to-cell transmissions, immune responses, and three delays
- Numerical scheme and analytical solutions to the stochastic nonlinear advection diffusion dynamical model
- On modeling column crystallizers and a Hermite predictor–corrector scheme for a system of integro-differential equations
- On a discrete fractional stochastic Grönwall inequality and its application in the numerical analysis of stochastic FDEs involving a martingale
- A new self adaptive Tseng’s extragradient method with double-projection for solving pseudomonotone variational inequality problems in Hilbert spaces
- Solitary waves of the RLW equation via least squares method
- Optical solitons and stability regions of the higher order nonlinear Schrödinger’s equation in an inhomogeneous fiber
- Weighted pseudo asymptotically Bloch periodic solutions to nonlocal Cauchy problems of integrodifferential equations in Banach spaces
- Modified inertial subgradient extragradient method for equilibrium problems
- Propagation of dark-bright soliton and kink wave solutions of fluidized granular matter model arising in industrial applications
- Existence and uniqueness of positive solutions for fractional relaxation equation in terms of ψ-Caputo fractional derivative
- Investigation of nonlinear fractional delay differential equation via singular fractional operator
- Travelling peakon and solitary wave solutions of modified Fornberg–Whitham equations with nonhomogeneous boundary conditions
- The (3 + 1)-dimensional Wazwaz–KdV equations: the conservation laws and exact solutions
- Stability and ψ-algebraic decay of the solution to ψ-fractional differential system
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Some new characterizations of a space curve due to a modified frame
- Numerical simulation of particulate matter propagation in an indoor environment with various types of heating
- Inertial accelerated algorithms for solving split feasibility with multiple output sets in Hilbert spaces
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Numerical solutions for variable-order fractional Gross–Pitaevskii equation with two spectral collocation approaches
- Threshold dynamics of an HIV-1 model with both virus-to-cell and cell-to-cell transmissions, immune responses, and three delays
- Numerical scheme and analytical solutions to the stochastic nonlinear advection diffusion dynamical model
- On modeling column crystallizers and a Hermite predictor–corrector scheme for a system of integro-differential equations
- On a discrete fractional stochastic Grönwall inequality and its application in the numerical analysis of stochastic FDEs involving a martingale
- A new self adaptive Tseng’s extragradient method with double-projection for solving pseudomonotone variational inequality problems in Hilbert spaces
- Solitary waves of the RLW equation via least squares method
- Optical solitons and stability regions of the higher order nonlinear Schrödinger’s equation in an inhomogeneous fiber
- Weighted pseudo asymptotically Bloch periodic solutions to nonlocal Cauchy problems of integrodifferential equations in Banach spaces
- Modified inertial subgradient extragradient method for equilibrium problems
- Propagation of dark-bright soliton and kink wave solutions of fluidized granular matter model arising in industrial applications
- Existence and uniqueness of positive solutions for fractional relaxation equation in terms of ψ-Caputo fractional derivative
- Investigation of nonlinear fractional delay differential equation via singular fractional operator
- Travelling peakon and solitary wave solutions of modified Fornberg–Whitham equations with nonhomogeneous boundary conditions
- The (3 + 1)-dimensional Wazwaz–KdV equations: the conservation laws and exact solutions
- Stability and ψ-algebraic decay of the solution to ψ-fractional differential system
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Some new characterizations of a space curve due to a modified frame
- Numerical simulation of particulate matter propagation in an indoor environment with various types of heating
- Inertial accelerated algorithms for solving split feasibility with multiple output sets in Hilbert spaces
- Stability analysis and abundant closed-form wave solutions of the Date–Jimbo–Kashiwara–Miwa and combined sinh–cosh-Gordon equations arising in fluid mechanics
- Contrasting effects of prey refuge on biodiversity of species
