A Double-Inertial Two-Subgradient Extragradient Algorithm for Solving Variational Inequalities with Minimum-Norm Solutions

Ioannis K. Argyros, Fouzia Amir, Habib ur Rehman () and Christopher Argyros
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Ioannis K. Argyros: Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Fouzia Amir: Center for Research and Innovation, Asia International University, Bukhara 200100, Uzbekistan
Habib ur Rehman: School of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Christopher Argyros: School of Computational Science and Engineering, Georgia Institute of Technology, 225 North Avenue NW, Atlanta, GA 30313, USA

Mathematics, 2025, vol. 13, issue 12, 1-26

Abstract: Variational inequality problems (VIPs) provide a versatile framework for modeling a wide range of real-world applications, including those in economics, engineering, transportation, and image processing. In this paper, we propose a novel iterative algorithm for solving VIPs in real Hilbert spaces. The method integrates a double-inertial mechanism with the two-subgradient extragradient scheme, leading to improved convergence speed and computational efficiency. A distinguishing feature of the algorithm is its self-adaptive step size strategy, which generates a non-monotonic sequence of step sizes without requiring prior knowledge of the Lipschitz constant. Under the assumption of monotonicity for the underlying operator, we establish strong convergence results. Numerical experiments under various initial conditions demonstrate the method’s effectiveness and robustness, confirming its practical advantages and its natural extension of existing techniques for solving VIPs.

Keywords: variational inequalities; two-subgradient extragradient method; monotone operators; inertial techniques; strong convergence; self-adaptive step sizes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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