A generalized iterative scheme for network design problem

This paper addresses a new optimization scheme designed for a continuous network design problem with respect to link capacity expansions. The network design problem can be formulated as a mathematical program with equilibrium constraints (MPEC) where the user equilibrium with variable demand is expressed as a variational inequality problem. Due to the non-differentiability of the perturbed solutions in equilibrium constraints, a non-smooth optimization model is established. A generalized bundle subgradient projection is presented to effectively solve the network design problem. Global convergence analysis for the proposed method is also delivered. Numerical calculations are conducted and promising results have shown potential of the proposed method in solving network design problem when compared to earlier studies.