Classical duality and existence results for amulti-criteria supply-demand network equilibrium model

Yunan Wu; T. C. Edwin Cheng

doi:10.3934/jimo.2009.5.615

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2009, Volume 5, Issue 3: 615-628. Doi: 10.3934/jimo.2009.5.615

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

Yunan Wu^1, and
T. C. Edwin Cheng^2,

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

Received: June 30, 2008

Revised: December 31, 2008

Published: June 2009

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Abstract

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.

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

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