This paper considers an iterative approximation of a common solution of a finite family of variational inequailties in a real reflexive Banach space. By employing the Bregman distance and projection methods, we propose an iterative algorithm which uses a newly constructed adaptive step size to avoid a dependence on the Lipschitz constants of the families of the cost operators. The algorithm is carefully constructed so that the need to find a farthest element in any of its iterate is avoided. A strong convergence theorem was proved using the proposed method. We report some numerical experiments to illustrate the performance of the algorithm and also compare with existing methods in the literature.
|Journal||Computational and Applied Mathematics|
|Publication status||Published - Sept 2022|
- Extragradient method
- Reflexive banach space
- Variational inequalities