July  2010, 6(3): 453-464. doi: 10.3934/jimo.2010.6.453

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, China

3. 

Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

Received  May 2009 Revised  March 2010 Published  June 2010

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.
Citation: Yunan Wu, Guangya Chen, T. C. Edwin Cheng. A vector network equilibrium problem with a unilateral constraint. Journal of Industrial & Management Optimization, 2010, 6 (3) : 453-464. doi: 10.3934/jimo.2010.6.453
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