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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
Autor principal: Hacıoğlu Emirhan
Otros Autores: Ertürk Müzeyyen, Faik, Gürsoy, Milovanović Gradimir V.
Publicado:
MDPI AG
Materias:
Iterative algorithms
Convergence
Inequalities
Algorithms
Machine learning
Hilbert space
Convexity
Iterative solution
Optimization
Acceso en línea:Citation/Abstract
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Resumen: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.
ISSN:2075-1680
DOI:10.3390/axioms14040288
Fuente:Engineering Database