American Institute of Mathematical Sciences

Advanced
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

Yunan Wu 1, and  T. C. Edwin Cheng 2,

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.
Keywords: Wardrop's equilibrium principle, Variational inequality, Network equilibrium, Duality..
Mathematics Subject Classification: Primary: 90C29, 90C35; Secondary: 90B06, 90B1.
Citation: Yunan Wu, T. C. Edwin Cheng. Classical duality and existence results for a multi-criteria supply-demand network equilibrium model. Journal of Industrial & Management Optimization, 2009, 5 (3) : 615-628. doi: 10.3934/jimo.2009.5.615
[1]

Annamaria Barbagallo, Rosalba Di Vincenzo, Stéphane Pia. On strong Lagrange duality for weighted traffic equilibrium problem. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1097-1113. doi: 10.3934/dcds.2011.31.1097
[2]

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
[3]

Liping Zhang. A nonlinear complementarity model for supply chain network equilibrium. Journal of Industrial & Management Optimization, 2007, 3 (4) : 727-737. doi: 10.3934/jimo.2007.3.727
[4]

Thomas Leroy. Relativistic transfer equations: Comparison principle and convergence to the non-equilibrium regime. Kinetic & Related Models, 2015, 8 (4) : 725-763. doi: 10.3934/krm.2015.8.725
[5]

Yu Chen. Delegation principle for multi-agency games under ex post equilibrium. Journal of Dynamics & Games, 2018, 5 (4) : 311-329. doi: 10.3934/jdg.2018019
[6]

Xiaona Fan, Li Jiang, Mengsi Li. Homotopy method for solving generalized Nash equilibrium problem with equality and inequality constraints. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1795-1807. doi: 10.3934/jimo.2018123
[7]

Hui-Qiang Ma, Nan-Jing Huang. Neural network smoothing approximation method for stochastic variational inequality problems. Journal of Industrial & Management Optimization, 2015, 11 (2) : 645-660. doi: 10.3934/jimo.2015.11.645
[8]

Dean A. Carlson. Finding open-loop Nash equilibrium for variational games. Conference Publications, 2005, 2005 (Special) : 153-163. doi: 10.3934/proc.2005.2005.153
[9]

O. Chadli, Z. Chbani, H. Riahi. Recession methods for equilibrium problems and applications to variational and hemivariational inequalities. Discrete & Continuous Dynamical Systems - A, 1999, 5 (1) : 185-196. doi: 10.3934/dcds.1999.5.185
[10]

Enkhbat Rentsen, Battur Gompil. Generalized nash equilibrium problem based on malfatti's problem. Numerical Algebra, Control & Optimization, 2019, 0 (0) : 0-0. doi: 10.3934/naco.2020022
[11]

Frank Jochmann. A variational inequality in Bean's model for superconductors with displacement current. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 545-565. doi: 10.3934/dcds.2009.25.545
[12]

T.C. Edwin Cheng, Yunan Wu. Henig efficiency of a multi-criterion supply-demand network equilibrium model. Journal of Industrial & Management Optimization, 2006, 2 (3) : 269-286. doi: 10.3934/jimo.2006.2.269
[13]

Hongming Yang, C. Y. Chung, Xiaojiao Tong, Pingping Bing. Research on dynamic equilibrium of power market with complex network constraints based on nonlinear complementarity function. Journal of Industrial & Management Optimization, 2008, 4 (3) : 617-630. doi: 10.3934/jimo.2008.4.617
[14]

Wenbin Wang, Peng Zhang, Junfei Ding, Jian Li, Hao Sun, Lingyun He. Closed-loop supply chain network equilibrium model with retailer-collection under legislation. Journal of Industrial & Management Optimization, 2019, 15 (1) : 199-219. doi: 10.3934/jimo.2018039
[15]

Ru Li, Guolin Yu. Strict efficiency of a multi-product supply-demand network equilibrium model. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2020065
[16]

Haodong Chen, Hongchun Sun, Yiju Wang. A complementarity model and algorithm for direct multi-commodity flow supply chain network equilibrium problem. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2020066
[17]

Qinglong Zhou, Yongchao Zhang. Analytic results for the linear stability of the equilibrium point in Robe's restricted elliptic three-body problem. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1763-1787. doi: 10.3934/dcds.2017074
[18]

Hongyu He, Naohiro Kato. Equilibrium submanifold for a biological system. Discrete & Continuous Dynamical Systems - S, 2011, 4 (6) : 1429-1441. doi: 10.3934/dcdss.2011.4.1429
[19]

Alain Chenciner. The angular momentum of a relative equilibrium. Discrete & Continuous Dynamical Systems - A, 2013, 33 (3) : 1033-1047. doi: 10.3934/dcds.2013.33.1033
[20]

Ricardo Almeida, Agnieszka B. Malinowska. Fractional variational principle of Herglotz. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2367-2381. doi: 10.3934/dcdsb.2014.19.2367

2018 Impact Factor: 1.025

Tools

Metrics

  • PDF downloads (23)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences