# American Institute of Mathematical Sciences

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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