# American Institute of Mathematical Sciences

October  2014, 10(4): 1019-1030. doi: 10.3934/jimo.2014.10.1019

## A power penalty method for the general traffic assignment problem with elastic demand

 1 School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China, China

Received  April 2013 Revised  August 2013 Published  February 2014

This paper established some new convergence results for the power penalty method for the nonlinear complementarity problem(NCP), and then applied the method to solve the general traffic assignment problem with elastic demand. The power penalty method approximates the NCP by a nonlinear equation containing a power penalty term. We prove that this method can handle general monotone NCPs. This result is important for the general traffic assignment problem with elastic demand because the associated NCP is often not $\xi$ monotone. This study considered the traffic assignment problem with symmetric and asymmetric link costs, as well as additive and non-additive route costs. We propose to use a column generation scheme based on the proposed power penalty method to solve this problem. Numerical results are provided to demonstrate the efficiency of the method.
Citation: Ming Chen, Chongchao Huang. A power penalty method for the general traffic assignment problem with elastic demand. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1019-1030. doi: 10.3934/jimo.2014.10.1019
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