On strong Lagrange duality for weighted traffic equilibrium problem

Annamaria Barbagallo; Rosalba Di Vincenzo; Stéphane Pia

doi:10.3934/dcds.2011.31.1097

Article Contents

2011, Volume 31, Issue 4: 1097-1113. Doi: 10.3934/dcds.2011.31.1097

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On strong Lagrange duality for weighted traffic equilibrium problem

1.
Department of Mathematics and Applications “R. Caccioppoli”, University of Naples “Federico II”, via Cintia, 80126 Naples
2.
Department of Mathematics and Computer Science, University of Catania, viale Andrea Doria n. 6, 95125 CATANIA

Received: September 30, 2009

Revised: March 31, 2010

Published: September 2011

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Abstract

The weighted traffic equilibrium problem introduced in [17], in which the equilibrium conditions have been expressed in terms of a weighted variational inequality, studies a transportation network in presence of congestion. For such a problem, existence and regularity theorems have been proved in [8]. In this paper, we analyze the dual problem and characterize the weighted traffic equilibrium solutions by means of Lagrange multipliers, which allow to describe the behavior of the weighted transportation network.

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Mathematics Subject Classification: Primary: 58E35, 90B20, 90C46; Secondary: 65K10.

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