# American Institute of Mathematical Sciences

July  2009, 5(3): 615-628. doi: 10.3934/jimo.2009.5.615

## Classical duality and existence results for a multi-criteria supply-demand network equilibrium model

 1 School of International Business, Beijing Foreign Studies University, Beijing 100089, China 2 Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

Received  July 2008 Revised  January 2009 Published  June 2009

We propose a dual model of a multi-criteria network equilibrium model and establish a primal-dual relationship between the network model and its dual model under certain generalized monotonicity assumptions. By using Gerstewitz's function, we obtain the primal-dual relationship without any convexity assumptions. As an application of the dual model, we derive an existence result for the network model.
Citation: Yunan Wu, T. C. Edwin Cheng. Classical duality and existence results for a multi-criteria supply-demand network equilibrium model. Journal of Industrial and Management Optimization, 2009, 5 (3) : 615-628. doi: 10.3934/jimo.2009.5.615
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