The convergence of diagonalization algorithms for asymmetric network equilibrium problems

We provide a sufficient condition for the convergence of diagonalization algorithms for equilibrium traffic assignment problems with asymmetric Jacobian matrix B(v) of the link user cost mapping s(v) of the flow v. When

Full-size image

, where D(v^*) > 0 is the diagonal of B(v^*) and v^* is the equilibrium flow, we demonstrate a local convergence theorem for nonlinear cost functions. The implication of this result for practical applications of the model are outlined.