# American Institute of Mathematical Sciences

December  2011, 31(4): 1097-1113. doi: 10.3934/dcds.2011.31.1097

## 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, Italy 2 Department of Mathematics and Computer Science, University of Catania, viale Andrea Doria n. 6, 95125 CATANIA, Italy, Italy

Received  October 2009 Revised  April 2010 Published  September 2011

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.
Citation: Annamaria Barbagallo, Rosalba Di Vincenzo, Stéphane Pia. On strong Lagrange duality for weighted traffic equilibrium problem. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1097-1113. doi: 10.3934/dcds.2011.31.1097
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