Flexible and Efficient Iterative Solutions for General Variational Inequalities in Real Hilbert Spaces
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| Publicado en: | Axioms vol. 14, no. 4 (2025), p. 288 |
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| Otros Autores: | , , |
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MDPI AG
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| Acceso en línea: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| 024 | 7 | |a 10.3390/axioms14040288 |2 doi | |
| 035 | |a 3194490183 | ||
| 045 | 2 | |b d20250101 |b d20251231 | |
| 084 | |a 231430 |2 nlm | ||
| 100 | 1 | |a Hacıoğlu Emirhan |u Department of Mathematics, Trakya University, 22030 Edirne, Türkiye; emirhanhacioglu@trakya.edu.tr | |
| 245 | 1 | |a Flexible and Efficient Iterative Solutions for General Variational Inequalities in Real Hilbert Spaces | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a This paper introduces a novel Picard-type iterative algorithm for solving general variational inequalities in real Hilbert spaces. The proposed algorithm enhances both the theoretical framework and practical applicability of iterative algorithms by relaxing restrictive conditions on parametric sequences, thereby expanding their scope of use. We establish convergence results, including a convergence equivalence with a previous algorithm, highlighting the theoretical relationship while demonstrating the increased flexibility and efficiency of the new approach. The paper also addresses gaps in the existing literature by offering new theoretical insights into the transformations associated with variational inequalities and the continuity of their solutions, thus paving the way for future research. The theoretical advancements are complemented by practical applications, such as the adaptation of the algorithm to convex optimization problems and its use in real-world contexts like machine learning. Numerical experiments confirm the proposed algorithm’s versatility and efficiency, showing superior performance and faster convergence compared to an existing method. | |
| 653 | |a Iterative algorithms | ||
| 653 | |a Convergence | ||
| 653 | |a Inequalities | ||
| 653 | |a Algorithms | ||
| 653 | |a Machine learning | ||
| 653 | |a Hilbert space | ||
| 653 | |a Convexity | ||
| 653 | |a Iterative solution | ||
| 653 | |a Optimization | ||
| 700 | 1 | |a Ertürk Müzeyyen |u Department of Mathematics, Adiyaman University, 02040 Adiyaman, Türkiye; merturk@adiyaman.edu.tr (M.E.); fgursoy@adiyaman.edu.tr (F.G.) | |
| 700 | 1 | |a Faik, Gürsoy |u Department of Mathematics, Adiyaman University, 02040 Adiyaman, Türkiye; merturk@adiyaman.edu.tr (M.E.); fgursoy@adiyaman.edu.tr (F.G.) | |
| 700 | 1 | |a Milovanović Gradimir V. |u Serbian Academy of Sciences and Arts, 11000 Belgrade, Serbia | |
| 773 | 0 | |t Axioms |g vol. 14, no. 4 (2025), p. 288 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3194490183/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3194490183/fulltextwithgraphics/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3194490183/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |