Interior Proximal and Multiplier Methods Based on Second Order Homogeneous Kernels
Mathematics of Operations Research
Nonadditive Shortest Paths: Subproblems in Multi-Agent Competitive Network Models
Computational & Mathematical Organization Theory
Journal of Optimization Theory and Applications
Computational study of state-of-the-art path-based traffic assignment algorithms
Mathematics and Computers in Simulation
A new modified Goldstein-Levitin-Polyakprojection method for variational inequality problems
Computers & Mathematics with Applications
Multi-objective and multi-constrained non-additive shortest path problems
Computers and Operations Research
Reformulating the traffic equilibrium problem via a smooth gap function
Mathematical and Computer Modelling: An International Journal
Computation and application of the paired combinatorial logit stochastic user equilibrium problem
Computers and Operations Research
A modified gradient projection algorithm for solving the elastic demand traffic assignment problem
Computers and Operations Research
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Gradient projection (GP) algorithm has been shown as an efficient algorithm for solving the traditional traffic equilibrium problem with additive route costs. Recently, GP has been extended to solve the nonadditive traffic equilibrium problem (NaTEP), in which the cost incurred on each route is not just a simple sum of the link costs on that route. However, choosing an appropriate stepsize, which is not known a priori, is a critical issue in GP for solving the NaTEP. Inappropriate selection of the stepsize can significantly increase the computational burden, or even deteriorate the convergence. In this paper, a self-adaptive gradient projection (SAGP) algorithm is proposed. The self-adaptive scheme has the ability to automatically adjust the stepsize according to the information derived from previous iterations. Furthermore, the SAGP algorithm still retains the efficient flow update strategy that only requires a simple projection onto the nonnegative orthant. Numerical results are also provided to illustrate the efficiency and robustness of the proposed algorithm.