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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 68, 2019 - Issue 11
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Articles

Existence and generic stability of solutions for multiclass multicriteria traffic equilibrium problems with capacity constraints of arcs

ORCID Icon, , &
Pages 2089-2097 | Received 04 May 2018, Accepted 15 Aug 2019, Published online: 31 Aug 2019

References

  • Wardrop J. Some theoretical aspects of road traffic research. Proc Inst Civil Eng Part II. 1952;1:325–378.
  • Khanh PQ, Luu LM. On the existence of solutions to vector quasivariational inequalities and quasicomplementarity problems with applications to traffic network equilibria. J Optim Theory Appl. 2004;123:533–548. doi: 10.1007/s10957-004-5722-3
  • Khanh PQ, Luu PQ. Some existence results for quasi-variational inequalities involving multifunctions and applications to traffic network equilibrium problems. J Global Optim. 2005;32:551–568. doi: 10.1007/s10898-004-2693-8
  • Lin Z. The study of traffic equilibrium problems with capacity constraints of arcs. Nonlinear Anal RWA. 2010;11:2280–2284. doi: 10.1016/j.nonrwa.2009.07.002
  • Lin Z. On existence of vector equilibrium flows with capacity constraints of arcs. Nonlinear Anal. 2010;72:2076–2079. doi: 10.1016/j.na.2009.10.007
  • Lin Z. An algorithm for traffic equilibrium flow with capacity constraints of arcs. J Transp Technol. 2015;5:240–246. doi: 10.4236/jtts.2015.54022
  • Dafermos SC. The traffic assignment problem for multiclass-user transportation networks. Transp Sci. 1972;6:73–87. doi: 10.1287/trsc.6.1.73
  • Li SJ, Chen GY. On relations between multiclass multicriteria traffic network equilibrium models and vector variational inequalities. J Syst Sci Syst Eng. 2006;15(3):284–297. doi: 10.1007/s11518-006-5012-8
  • Nagurney A. A multiclass, multicriteria traffic network equilibrium model. Math Comput Model. 2000;32:393–411. doi: 10.1016/S0895-7177(00)00142-4
  • Nagurney A, Dong J. A multiclass, multicriteria traffic network equilibrium model with elastic demand. Transp Res B. 2002;36:445–469. doi: 10.1016/S0191-2615(01)00013-3
  • Yang H, Huang HJ. The multi-class, multi-criteria traffic network equilibrium and systems optimum problem. Transp Res B. 2004;38:1–15. doi: 10.1016/S0191-2615(02)00074-7
  • Zhang XN, Yang H, Huang HJ. Multiclass multicriteria mixed equilibrium on networks and uniform link tolls for system optimum. Eur J Oper Res. 2008;189:146–158. doi: 10.1016/j.ejor.2007.05.004
  • Luc DT, Phuong TTT. Equilibrium in multi-criteria transportation networks. J Optim Theory Appl. 2016;169(1):116–147. doi: 10.1007/s10957-016-0876-3
  • Tian XQ, Xu YD. Traffic network equilibrium problems with capacity constraints of arcs and linear scalarization methods. J Appl Math. 2012 2012, Article ID 612142, 12 p. doi:10.1155/2012/612142.
  • Xu YD, Li SJ, Teo KL. Vector network equilibrium problems with capacity constraints of arcs. Transp Res E. 2012;48:567–577. doi: 10.1016/j.tre.2011.11.002
  • Xu YD, Li SJ. Optimality conditions for generalized Ky Fan quasi-inequalities with applications. J Optim Theory Appl. 2013;157:663–684. doi: 10.1007/s10957-012-0242-z
  • Truong TTP, Luc DT. Equilibrium in multi-criteria supply and demand networks with capacity constraints. Math Methods Oper Res. 2015;81:83–107. doi: 10.1007/s00186-014-0487-4
  • Browder FE. The fixed point theory of multi-valued mappings in topological vector spaces. Math Ann. 1968;177:283–301. doi: 10.1007/BF01350721
  • Fan K. A generalization of Tychonoff's fixed point theorem. Math Ann. 1961;142:305–310. doi: 10.1007/BF01353421
  • Fort MK. Points of continuity of semicontinuous functions. Publ Math Debrecen. 1951;2:100–102.

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