An Alternated Inertial Projection Algorithm for Multi-Valued Variational Inequality and Fixed Point Problems

Abstract

In this paper, we propose an alternated inertial projection algorithm for solving multi-valued variational inequality problem and fixed point problem of demi-contractive mapping. On one hand, this algorithm only requires the mapping is pseudo-monotone. On the other hand, this algorithm is combined with the alternated inertial method to accelerate the convergence speed. The global convergence of the algorithm can be obtained under mild conditions. Preliminary numerical results show that the convergence speed of our algorithm is faster than some existing algorithms.

Keywords

• alternated inertial method
• multi-valued variational inequality
• pseudo-monotonicity
• convergence speed
• fixed point