A Double-Inertial Two-Subgradient Extragradient Algorithm for Solving Variational Inequalities with Minimum-Norm Solutions
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. T...
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2025-06-01
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| author | Ioannis K. Argyros Fouzia Amir Habib ur Rehman Christopher Argyros |
| author_facet | Ioannis K. Argyros Fouzia Amir Habib ur Rehman Christopher Argyros |
| author_sort | Ioannis K. Argyros |
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| description | 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. |
| format | Article |
| id | doaj-art-8ee205aef5874cafadf8ce38cacd3b9a |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-8ee205aef5874cafadf8ce38cacd3b9a2025-08-20T03:27:22ZengMDPI AGMathematics2227-73902025-06-011312196210.3390/math13121962A Double-Inertial Two-Subgradient Extragradient Algorithm for Solving Variational Inequalities with Minimum-Norm SolutionsIoannis K. Argyros0Fouzia Amir1Habib ur Rehman2Christopher Argyros3Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USACenter for Research and Innovation, Asia International University, Bukhara 200100, UzbekistanSchool of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaSchool of Computational Science and Engineering, Georgia Institute of Technology, 225 North Avenue NW, Atlanta, GA 30313, USAVariational 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.https://www.mdpi.com/2227-7390/13/12/1962variational inequalitiestwo-subgradient extragradient methodmonotone operatorsinertial techniquesstrong convergenceself-adaptive step sizes |
| spellingShingle | Ioannis K. Argyros Fouzia Amir Habib ur Rehman Christopher Argyros A Double-Inertial Two-Subgradient Extragradient Algorithm for Solving Variational Inequalities with Minimum-Norm Solutions Mathematics variational inequalities two-subgradient extragradient method monotone operators inertial techniques strong convergence self-adaptive step sizes |
| title | A Double-Inertial Two-Subgradient Extragradient Algorithm for Solving Variational Inequalities with Minimum-Norm Solutions |
| title_full | A Double-Inertial Two-Subgradient Extragradient Algorithm for Solving Variational Inequalities with Minimum-Norm Solutions |
| title_fullStr | A Double-Inertial Two-Subgradient Extragradient Algorithm for Solving Variational Inequalities with Minimum-Norm Solutions |
| title_full_unstemmed | A Double-Inertial Two-Subgradient Extragradient Algorithm for Solving Variational Inequalities with Minimum-Norm Solutions |
| title_short | A Double-Inertial Two-Subgradient Extragradient Algorithm for Solving Variational Inequalities with Minimum-Norm Solutions |
| title_sort | double inertial two subgradient extragradient algorithm for solving variational inequalities with minimum norm solutions |
| topic | variational inequalities two-subgradient extragradient method monotone operators inertial techniques strong convergence self-adaptive step sizes |
| url | https://www.mdpi.com/2227-7390/13/12/1962 |
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