In this paper, properties of differentiable gap functions for variational inequalities and convergence of the corresponding descent methods under a Hilbert space setting are considered. We give various convergence results under different assumptions on the cost mapping, including the monotone...

How reliable the transport network is greatly affects the mobility and economy of a country. To assess the reliability of the network accurately and design a reliable transport network properly, one should consider the risk taking and elastic behaviour of travel demand. This paper develops a...

The continuous network design problem (CNDP) is generally formulated as a mathematical program with equilibrium constraints (MPEC). It aims to optimize the network performance via expansion of existing links subject to the Wardrop user equilibrium constraint. As one of the extremely challenging...

The paper deals with equilibrium problems (EPs) with nonlinear convex constraints. First, EP is reformulated as a global optimization problem introducing a class of gap functions, in which the feasible set of EP is replaced by a polyhedral approximation. Then, an algorithm is given for solving...