An iterative algorithm for solving generalized variational inequality problems and fixed point problems

Abstract

We propose an iterative scheme for finding a common element of fixed points set of a nonexpansive mapping and the solutions set of a generalized variational inequality problem in Euclidean space . Under some mild conditions, we establish the convergence theorem for the proposed algorithm. We also give a suitable condition to ensure the intersection of fixed points set of a nonexpansive mapping and the solutions set of a generalized variational inequality problem to be nonempty. In addition, under certain error bound conditions, we prove the convergence rate of the iterative sequence. Preliminary computational experience is also reported.

Keywords:

• generalized variational inequality
• hyperplane
• Armijo-type linesearch
• nonexpansive mapping
• fixed point

AMS Subject Classifications:

• 90C25
• 49J40
• 90C33

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 10671135]; the Key Project of Chinese Ministry of Education [grant number 212147]. The work of the third author was partially supported by the Grant NSC [grant number 103-2923-E-037-001-MY3].