Algorithms and Inertial Algorithms for Inverse Mixed Variational Inequality Problems in Hilbert Spaces

Abstract

The inverse mixed variational inequality problem comes from classical variational inequality, and it has many applications. In this paper, we propose new algorithms to study the inverse mixed variational inequality problems in Hilbert spaces, and these algorithms are based on the generalized projection operator. Next, we establish convergence theorems under inverse strong monotonicity conditions. In addition, we also provide inertial-type algorithms for the inverse mixed variational inequality problems with conditions that differ from the above convergence theorems.

Keywords

• variational inequality
• inverse variational inequality
• inverse strong monotonicity
• inertial algorithm
• generalized projection