The projection algorithm for inverse quasi-variational inequalities with applications to traffic assignment and network equilibrium control problems

We consider a first-order dynamical system for solving inverse quasi-variational inequalities in finite dimensional spaces. Through an explicit time discrete version of the proposed dynamical system, we investigate the linear convergence of a projection algorithm under suitable conditions of parameters. Moreover, we investigate the application of inverse quasi-variational inequalities in traffic assignment problem and network equilibrium control problem. The numerical experiments for these practical problems confirm the linear convergence of the theoretical part. In particular, the obtained results provide a positive answer to an open question posted by S. Dey and S. Reich in Optimization, DOI: 10.1080/02331934.2023.2173525 (2023).