Advanced Algorithms and Common Solutions to Variational Inequalities

• Main Authors: Hasanen A. Hammad, Habib ur Rehman, Manuel De la Sen
• Format: Article
• Language: English
• Published: MDPI AG 2020-07-01
• Series: Symmetry
• Subjects: variational inequality; hybrid method; parallel computation; sub-gradient extra-gradient inertial method; cyclic inertial algorithm
• Online Access: https://www.mdpi.com/2073-8994/12/7/1198

The paper aims to present advanced algorithms arising out of adding the inertial technical and shrinking projection terms to ordinary parallel and cyclic hybrid inertial sub-gradient extra-gradient algorithms (for short, PCHISE). Via these algorithms, common solutions of variational inequality problems (CSVIP) and strong convergence results are obtained in Hilbert spaces. The structure of this problem is to find a solution to a system of unrelated VI fronting for set-valued mappings. To clarify the acceleration, effectiveness, and performance of our parallel and cyclic algorithms, numerical contributions have been incorporated. In this direction, our results unify and generalize some related papers in the literature.