Double inertial steps extragadient-type methods for solving optimal control and image restoration problems

Austine Efut Ofem*, Jacob Ashiwere Abuchu, Godwin Chidi Ugwunnadi, Hossam A. Nabwey*, Abubakar Adamu, Ojen Kumar Narain

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In order to approximate the common solution of quasi-nonexpansive fixed point and pseudo-monotone variational inequality problems in real Hilbert spaces, this paper presented three new modified sub-gradient extragradient-type methods. Our algorithms incorporated viscosity terms and double inertial extrapolations to ensure strong convergence and to speed up convergence. No line search methods of the Armijo type were required by our algorithms. Instead, they employed a novel self-adaptive step size technique that produced a non-monotonic sequence of step sizes while also correctly incorporating a number of well-known step sizes. The step size was designed to lessen the algorithms' reliance on the initial step size. Numerical tests were performed, and the results showed that our step size is more effective and that it guarantees that our methods require less execution time. We stated and proved the strong convergence of our algorithms under mild conditions imposed on the control parameters. To show the computational advantage of the suggested methods over some well-known methods in the literature, several numerical experiments were provided. To test the applicability and efficiencies of our methods in solving real-world problems, we utilized the proposed methods to solve optimal control and image restoration problems.

Original languageEnglish
Pages (from-to)12870-12905
Number of pages36
JournalAIMS Mathematics
Volume9
Issue number5
DOIs
Publication statusPublished - 2024
Externally publishedYes

Keywords

  • fixed point
  • pseudo-monotone operator
  • strong convergence
  • subgradient extragradient method
  • variational inequality problem
  • viscosity

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