Finite Convergence and Weak Sharpness for General Split Variational Inequalities with Application to Traffic Equilibrium

Abstract In this paper, we study a general split variational inequality problem and investigate the weak sharpness property of its solution set. We also discuss the finite convergence property of a sequence converging to the solution set based on the weak sharpness property. In addition, we introduce an iterative method that converges to the solution set of the considered problem. Then, we formulate the traffic network equilibrium of two cities over an extended period in terms of our considered problem and establish some existence results. Finally, we validate our findings with a numerical example.