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Peer-reviewedCC BY 4.0Mathematics

Weak and Error-Bound Linear Convergence of a Safeguarded Anderson-Accelerated Subgradient Extragradient Method

  • Austine Efut Ofem1
  • Adhir Maharaj2
  • Virath Singh3
  1. 1Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0001, South Africa
  2. 2Department of Mathematics, Durban University of Technology, Durban 4000, South Africa
  3. 3School of Agriculture and Science, University of KwaZulu-Natal, Durban 4000, South Africa
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Abstract

We propose a safeguarded Anderson-accelerated subgradient extragradient method for variational inequalities in real Hilbert spaces. The method combines classical projection onto the feasible set with an explicit projection onto a supporting half space and finite memory Anderson correction. A self-adaptive step size with a summable additive recovery sequence is used without prior knowledge of the Lipschitz constant. Weak convergence is established under a solution-oriented condition that does not require monotonicity or pseudomonotonicity. Under a local projection-residual error bound, we obtain Q-linear convergence of the distance to the solution set and strong R-linear convergence of the iterates without assuming uniqueness. Numerical experiments on a dense nonlinear orthogonal transform variational inequality, and a dense nonlinear network consensus model illustrates the performance of the method.

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Cite

BibTeXRIS
BibTeX
@article{ofem2026weak,
  title = {{Weak and Error-Bound Linear Convergence of a Safeguarded Anderson-Accelerated Subgradient Extragradient Method}},
  author = {Austine Efut Ofem and Adhir Maharaj and Virath Singh},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14193633},
  url = {https://www.mdpi.com/2227-7390/14/19/3633},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Weak and Error-Bound Linear Convergence of a Safeguarded Anderson-Accelerated Subgradient Extragradient Method
AU  - Austine Efut Ofem
AU  - Adhir Maharaj
AU  - Virath Singh
PY  - 2026
DA  - 2026/10/08
JO  - Mathematics
DO  - 10.3390/math14193633
UR  - https://www.mdpi.com/2227-7390/14/19/3633
AB  - We propose a safeguarded Anderson-accelerated subgradient extragradient method for variational inequalities in real Hilbert spaces. The method combines classical projection onto the feasible set with an explicit projection onto a supporting half space and finite memory Anderson correction. A self-adaptive step size with a summable additive recovery sequence is used without prior knowledge of the Lipschitz constant. Weak convergence is established under a solution-oriented condition that does not require monotonicity or pseudomonotonicity. Under a local projection-residual error bound, we obtain Q-linear convergence of the distance to the solution set and strong R-linear convergence of the iterates without assuming uniqueness. Numerical experiments on a dense nonlinear orthogonal transform variational inequality, and a dense nonlinear network consensus model illustrates the performance of the method.
SN  - 2227-7390
ER  -