Linear convergence of forward-backward-forward type methods

Duong Viet Thong; Duong Viet Thong

doi:10.3934/jimo.2026015

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 1: 405-421. doi: 10.3934/jimo.2026015

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Research article

Linear convergence of forward-backward-forward type methods

Duong Viet Thong ^, ,

Fundamental Sciences Faculty, National Economics University, Hanoi City, Vietnam

Received: 15 October 2024 Revised: 17 November 2025 Accepted: 20 November 2025 Published: 04 December 2025
47H09, 47H10, 47J20, 47J25

This article is motivated by the work of Tseng (SIAM J. Control Optim. 38, 431–446 (2020)). We study some forward-backward-forward-type methods for solving variational inclusion problems involving the sum of two operators in real Hilbert spaces. We establish strong convergence theorems for these methods, demonstrating convergence to the unique solution of the problem with an R-linear rate, without relying on a line search procedure or Tseng's regularity assumptions.
- forward-backward-forward method,
- strongly monotone,
- convergence rate,
- zero point,
- R-linear rate
Citation: Duong Viet Thong. Linear convergence of forward-backward-forward type methods[J]. Journal of Industrial and Management Optimization, 2026, 22(1): 405-421. doi: 10.3934/jimo.2026015

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Abstract

This article is motivated by the work of Tseng (SIAM J. Control Optim. 38, 431–446 (2020)). We study some forward-backward-forward-type methods for solving variational inclusion problems involving the sum of two operators in real Hilbert spaces. We establish strong convergence theorems for these methods, demonstrating convergence to the unique solution of the problem with an R-linear rate, without relying on a line search procedure or Tseng's regularity assumptions.

References

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