A class of strongly convergent subgradient extragradient methods for solving quasimonotone variational inequalities

• Autorzy: Rehman Habib ur , Kumam Poom , Ozdemir Murat , Yildirim Isa , Kumam Wiyada

Identyfikatory

DOI

10.1515/dema-2022-0202

• Języki publikacji: EN

Abstrakty

EN

The primary goal of this research is to investigate the approximate numerical solution of variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In this study, the sequence obtained by the proposed iterative technique for solving quasimonotone variational inequalities converges strongly toward a solution due to the viscosity-type iterative scheme. Furthermore, a new technique is proposed that uses an inertial mechanism to obtain strong convergence iteratively without the requirement for a hybrid version. The fundamental benefit of the suggested iterative strategy is that it substitutes a monotone and non-monotone step size rule based on mapping (operator) information for its Lipschitz constant or another line search method. This article also provides a numerical example to demonstrate how each method works.

Słowa kluczowe

EN

variational inequality problem; subgradient extragradient method; strong convergence result; quasimonotone operator; Lipschitz continuity

PL

nierówność wariacyjna; konwergencja; operator quasi-monotoniczny; ciągłość Lipschitza

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20220202
• Opis fizyczny: Bibliogr. 39 poz., tab.

Twórcy

autor

Rehman Habib ur

• Department of Mathematics, Faculty of Science, Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand

autor

Kumam Poom

• Department of Mathematics, Faculty of Science, Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand

autor

Ozdemir Murat

• Department of Mathematics, Ataturk University, Erzurum 25240, Turkey

autor

Yildirim Isa

• Department of Mathematics, Ataturk University, Erzurum 25240, Turkey

autor

Kumam Wiyada

• Department of Mathematics and Computer Science, Faculty of Science and Technology, Applied Mathematics for Science and Engineering Research Unit (AMSERU), Program in Applied Statistics, Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani 12110, Thailand

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).