Solving nonadditive traffic assignment problems:A self-adaptive projection-auxiliary problem method for variationalinequalities

Gang Qian; Deren Han; Lingling Xu; Hai Yang

doi:10.3934/jimo.2013.9.255

Article Contents

2013, Volume 9, Issue 1: 255-274. Doi: 10.3934/jimo.2013.9.255

This issue Previous Article An outcome space algorithm for minimizing the product of two convex functions over a convex set Next Article

Solving nonadditive traffic assignment problems: A self-adaptive projection-auxiliary problem method for variational inequalities

1.
School of Computer Sciences, Nanjing Normal University, Nanjing 210097
2.
School of Mathematical Science, Nanjing Normal University, Nanjing 210046
3.
School of Mathematical Sciences, Key Laboratory for NSLSCS of Jiangsu Province, Nanjing Normal University, Nanjing 210046
4.
Department of Civil Engineering, The Hong Kong University of Science and Technology, Hong Kong

Received: December 31, 2011

Revised: May 31, 2012

Published: December 2012

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Abstract

In the last decade, as calibrations of the classical traffic equilibrium problems, various models of traffic equilibrium problems with nonadditive route costs have been proposed. For solving such models, this paper develops a self-adaptive projection-auxiliary problem method for monotone variational inequality (VI) problems. It first converts the original problem where the feasible set is the intersection of a linear manifold and a simple set to an augmented VI with simple set, which makes the projection easy to implement. The self-adaptive strategy avoids the difficult task of choosing `suitable' parameters, and leads to fast convergence. Under suitable conditions, we prove the global convergence of the method. Some preliminary computational results are presented to illustrate the ability and efficiency of the method.

Keywords:

Traffic equilibrium and nonadditive cost,
variational inequality problem,
auxiliary problem principle,
projection method,
self-adaptive strategy.

Mathematics Subject Classification: Primary: 90C33; Secondary: 90B20, 93B40.

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