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A new self-adaptive inertial CQ-algorithm for solving convex feasibility and monotone inclusion problems

  • Cyril D. Enyi , Olaniyi S. Iyiola ORCID logo EMAIL logo and Chinedu G. Ezea
Published/Copyright: October 14, 2022
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International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 24 Issue 8

Abstract

Using a dynamical step size technique, a new self-adaptive CQ-algorithm is proposed in the presence of an inertial term to find the solution of convex feasibility problem and monotone inclusion problem involving a finite number of maximal monotone set valued operators. To do this, in certain Banach spaces, we construct an algorithm which converges to the fixed point of right Bregman strongly nonexpansive mappings and coincidentally solves the convex feasibility and monotone inclusion problems. Strong convergence of the algorithm is achieved without computation of the associated operator norms. Interesting numerical examples which illustrate the implementation and efficiency of our scheme are also given. Results obtained via this work improve and extend on previous results of its kind, in the literature.

Keywords: Bregman mapping; convex feasibility problem; inertial technique; monotone inclusion; split feasibility problem
2010 AMS MS Classifications: 47H06; 47H09; 47J05; 47J25
Corresponding author: Olaniyi S. Iyiola, Department of Mathematics, Clarkson University, Potsdam, NY, USA, E-mail: ,

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2021-08-12
Revised: 2022-08-22
Accepted: 2022-09-29
Published Online: 2022-10-14

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Testing of logarithmic-law for the slip with friction boundary condition
  4. A new clique polynomial approach for fractional partial differential equations
  5. The modified Rusanov scheme for solving the phonon-Bose model
  6. Delta-shock for a class of strictly hyperbolic systems of conservation laws
  7. The Cădariu–Radu method for existence, uniqueness and Gauss Hypergeometric stability of a class of Ξ-Hilfer fractional differential equations
  8. Novel periodic and optical soliton solutions for Davey–Stewartson system by generalized Jacobi elliptic expansion method
  9. The simulation of two-dimensional plane problems using ordinary state-based peridynamics
  10. Reduced basis method for the nonlinear Poisson–Boltzmann equation regularized by the range-separated canonical tensor format
  11. Simulation of the crystallization processes by population balance model using a linear separation method
  12. PS and GW optimization of variable sliding gains mode control to stabilize a wind energy conversion system under the real wind in Adrar, Algeria
  13. Characteristics of internal flow of nozzle integrated with aircraft under transonic flow
  14. Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field
  15. The influence pulse-like near-field earthquakes on repairability index of reversible in mid-and short-rise buildings
  16. Intelligent controller for maximum power extraction of wind generation systems using ANN
  17. A new self-adaptive inertial CQ-algorithm for solving convex feasibility and monotone inclusion problems
  18. Existence and Hyers–Ulam stability of solutions for nonlinear three fractional sequential differential equations with nonlocal boundary conditions
  19. A study on solvability of the fourth-order nonlinear boundary value problems
  20. Adaptive control for position and force tracking of uncertain teleoperation with actuators saturation and asymmetric varying time delays
  21. Framing the hydrothermal significance of water-based hybrid nanofluid flow over a revolving disk
  22. Catalytic surface reaction on a vertical wavy surface placed in a non-Darcy porous medium
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  24. Corrigendum
  25. Corrigendum to: numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
https://doi.org/10.1515/ijnsns-2021-0322
Keywords for this article
Bregman mapping; convex feasibility problem; inertial technique; monotone inclusion; split feasibility problem

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Testing of logarithmic-law for the slip with friction boundary condition
  4. A new clique polynomial approach for fractional partial differential equations
  5. The modified Rusanov scheme for solving the phonon-Bose model
  6. Delta-shock for a class of strictly hyperbolic systems of conservation laws
  7. The Cădariu–Radu method for existence, uniqueness and Gauss Hypergeometric stability of a class of Ξ-Hilfer fractional differential equations
  8. Novel periodic and optical soliton solutions for Davey–Stewartson system by generalized Jacobi elliptic expansion method
  9. The simulation of two-dimensional plane problems using ordinary state-based peridynamics
  10. Reduced basis method for the nonlinear Poisson–Boltzmann equation regularized by the range-separated canonical tensor format
  11. Simulation of the crystallization processes by population balance model using a linear separation method
  12. PS and GW optimization of variable sliding gains mode control to stabilize a wind energy conversion system under the real wind in Adrar, Algeria
  13. Characteristics of internal flow of nozzle integrated with aircraft under transonic flow
  14. Magnetogasdynamic shock wave propagation using the method of group invariance in rotating medium with the flux of monochromatic radiation and azimuthal magnetic field
  15. The influence pulse-like near-field earthquakes on repairability index of reversible in mid-and short-rise buildings
  16. Intelligent controller for maximum power extraction of wind generation systems using ANN
  17. A new self-adaptive inertial CQ-algorithm for solving convex feasibility and monotone inclusion problems
  18. Existence and Hyers–Ulam stability of solutions for nonlinear three fractional sequential differential equations with nonlocal boundary conditions
  19. A study on solvability of the fourth-order nonlinear boundary value problems
  20. Adaptive control for position and force tracking of uncertain teleoperation with actuators saturation and asymmetric varying time delays
  21. Framing the hydrothermal significance of water-based hybrid nanofluid flow over a revolving disk
  22. Catalytic surface reaction on a vertical wavy surface placed in a non-Darcy porous medium
  23. Carleman framework filtering of nonlinear noisy phase-locked loop system
  24. Corrigendum
  25. Corrigendum to: numerical modeling of thermal influence to pollutant dispersion and dynamics of particles motion with various sizes in idealized street canyon
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