A vector network equilibrium problem with a unilateralconstraint

Yunan Wu; Guangya Chen; T. C. Edwin Cheng

doi:10.3934/jimo.2010.6.453

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2010, Volume 6, Issue 3: 453-464. Doi: 10.3934/jimo.2010.6.453

This issue Previous Article Next Article Levitin-Polyak well-posedness for variational inequalities and for optimization problems with variational inequality constraints

A vector network equilibrium problem with a unilateral constraint

1.
School of International Business, Beijing Foreign Studies University, Beijing 100089
2.
Academy of Mathematics and Systems Science, Institute of Systems Science, Chinese Academy of sciences, Beijing 100089
3.
Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received: April 30, 2009

Revised: February 28, 2010

Published: June 2010

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Abstract

We formulate a network equilibrium model with a unilateral constraint based on Wardrop's principle and establish that the model is equivalent to a quasi-variational inequality. For the case with vector cost functions, we use Gerstewitz's function to derive two equivalence relations between the vector network equilibrium model with a unilateral constraint and quasi-variational inequalities without any convexity assumptions.

Keywords:

Network equilibrium; Variational inequality; Wardrop's equilibrium principle.

Mathematics Subject Classification: Primary: 90C29, 90C35; Secondary: 90B06, 90B10.

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