A Hybrid Inertial Method for Variational Inequalities with Applications to Traffic Flow Models

Abstract

In this paper, we introduce a hybrid inertial algorithm for solving variational inequality problems and split common fixed point problems in real Hilbert spaces. The proposed method combines inertial and viscosity techniques within a unified framework and extends several existing iterative schemes. Under appropriate conditions, we establish strong convergence of the generated sequence. As applications, we consider the generalized split feasibility problem and convex minimization. A numerical example arising from traffic flow modeling is presented to demonstrate the effectiveness of the proposed method.