Skip to main content
SpringerLink
Log in

Improved Noniterative Algorithm for Solving the Traffic Equilibrium Problem

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

We provide an equivalent formulation of a previously proposed noniterative algorithm (see A. Maugeri, Appl. Math. Optim. 16, 169–185, 1987) for the traffic equilibrium problem. Moreover, under the strict monotonicity assumption, we provide an improved algorithm which enlarges the range of applicability of the previous algorithm and decreases considerably its computational effort. Our algorithm is based on a general algorithm for variational inequalities (see O. Mancino, G. Stampacchia, J. Optim. Theory Appl. 9, 3–23, 1972), which we further develop and adapt to the traffic equilibrium problem. Both our proofs and the algorithm exploit directly the equilibrium conditions which characterize our problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Maugeri, A.: Convex programming, variational inequalities, and applications to the traffic equilibrium problem. Appl. Math. Optim. 16, 169–185 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  2. Mancino, O., Stampacchia, G.: Convex programming and variational inequalities. J. Optim. Theory Appl. 9, 3–23 (1972)

    Article  MathSciNet  Google Scholar 

  3. Giannessi, F., Maugeri, A. (eds.): Variational Inequalities and Network Equilibrium Problems. Plenum, New York (1995)

    MATH  Google Scholar 

  4. Facchinei, F., Pang, J.S.: Finite-Dimensional Variational Inequalities and Complementarity Problems. Springer, New York (2003)

    Google Scholar 

  5. Dafermos, S.: Traffic equilibrium and variational inequalities. Transp. Sci. 14, 42–54 (1980)

    Article  MathSciNet  Google Scholar 

  6. Patriksson, M.: The Traffic Assignment Problem. VSP, Utrecht (1994)

    Google Scholar 

  7. Smith, M.J.: The existence, uniqueness and stability of traffic equilibrium. Transp. Res. 138, 295–304 (1979)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Engineering, University of Catania, Catania, Italy

    F. Raciti

  2. Department of Physics, University of Catania, Catania, Italy

    P. Falsaperla

Authors
  1. F. Raciti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Falsaperla
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Raciti.

Additional information

Communicated by F. Giannessi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Raciti, F., Falsaperla, P. Improved Noniterative Algorithm for Solving the Traffic Equilibrium Problem. J Optim Theory Appl 133, 401–411 (2007). https://doi.org/10.1007/s10957-007-9230-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-007-9230-0

Keywords

Search

Navigation