A relaxed inertial projection algorithm for solving inverse quasi-variational inequalities and its application to traffic assignment

In this article, we propose a relaxed inertial projection algorithm for solving inverse quasi-variational inequality problems (IQVIPs) in real Hilbert spaces. The method integrates inertial extrapolation and relaxation techniques to accelerate the convergence of the classical projection scheme. Strong convergence to the unique solution is established under standard monotonicity and Lipschitz continuity assumptions on the operator, covering both the moving-set case and the fully general set-valued constraint setting. Numerical comparisons with an existing algorithm show that the proposed method converges significantly faster, requires fewer iterations, and incurs lower computational cost over a wide range of initial points. The practical effectiveness of the approach is further demonstrated through an application to a realistic continuous-time road pricing problem on a four-bridge traffic network, where the algorithm efficiently computes equilibrium tolls that achieve the desired flow redistribution while respecting toll-dependent capacity constraints. These results confirm the robustness of the proposed method and its potential for solving structured equilibrium models arising in transportation and related fields