S-iterative algorithm for solving variational inequalities

Abstract

In this paper we propose an S-iterative algorithm for finding the common element of the set of solutions of the variational inequalities and the set of fixed points of nonexpansive mappings. We study the convergence criteria of the mentioned algorithm under some mild conditions. As an application, a modified algorithm is suggested to solve convex minimization problems. Numerical examples are given to validate the theoretical findings obtained herein. Our results may be considered as an improvement, refinement and complement of the previously known results.

Keywords:

• S-iterative algorithm
• convergence
• rate of convergence
• variational inequality
• nonexpansive mappings
• convex optimization

2010 Mathematics Subject Classifications:

• 49J40
• 58E35
• 47H10

Disclosure statement

No potential conflict of interest was reported by the authors.