Work

Image and signal recovery via a novel alternating golden ratio two-subgradient extragradient method

Year: 2025

Type: article

Abstract: We introduce and analyze a novel two-subgradient extragradient method (TSEGM) for solving monotone variational inequality problems (VIPs) in real Hilbert spaces. Building on recent advances in extragradient-based schemes, the proposed algorithm enhances the classical TSEGM by integrating an alternating golden ratio mechanism, thereby eliminating reliance on computationally intensive linesearch procedures. A central feature of our method is a self-adaptive step-size rule that dynamically adjusts and may increase the step size during the iterations, improving both convergence efficiency and numerical stability. Under standard assumptions, we establish weak convergence and an R -linear convergence rate to a solution of the VIP governed by a monotone operator. Extensive numerical experiments demonstrate that the proposed algorithm outperforms several state-of-the-art methods in terms of speed and computational efficiency. Applications to image restoration and signal recovery further illustrate the practicality and robustness of the approach.

Source: Ain Shams Engineering Journal

DOI: 10.1016/j.asej.2025.103876

Authors: Habib ur Rehman, Kamonrat Sombut, Hasanen A. Hammad, Thidaporn Seangwattana

Institutions: Yunnan Normal University, King Mongkut's University of Technology North Bangkok, Rajamangala University of Technology, Qassim University, Sohag University

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funder: King Mongkut's University of Technology North Bangkok