Skip to main content
SpringerLink
Log in

The Differential Variational Inequality Formulation of Dynamic User Equilibria

  • Chapter
  • First Online:
Dynamic Network User Equilibrium

Part of the book series: Complex Networks and Dynamic Systems ((CNDS,volume 5))

  • 140 Accesses

Abstract

In this chapter, we present the differential variational inequality (DVI) formalism and use it to relate the much studied calculus of variations, including the theory of optimal control, to differential Nash games. The games we consider are motivated by the notion of dynamic user equilibrium as presented in the previous chapter.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References and Suggested Reading

  • Friesz, T. L. (2010). Dynamic optimization and differential games. New York: Springer.

    Book  Google Scholar 

  • Friesz, T. L., Bernstein, D., Smith, T., Tobin, R., & Wie, B. (1993). A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research, 41(1), 80–91.

    Article  Google Scholar 

  • Friesz, T. L., Kim, T., Kwon, C., & Rigdon, M. A. (2011). Approximate network loading and dual-time-scale dynamic user equilibrium. Transportation Research Part B, 45(1), 176–207.

    Article  Google Scholar 

  • Friesz, T. L., & Meiman, A. (2014). Dynamic user equilibria with elastic demand. Transportmetrica A: Transport Science, 10(7), 661–668.

    Article  Google Scholar 

  • Luenberger, D. G. (1984). Linear and nonlinear programming. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Mangasarian, O. (1969). Nonlinear programming. New York: McGraw-Hill.

    Google Scholar 

  • Pang, J. S., & Stewart, D. E. (2008). Differential variational inequalities. Mathematical Programming, Series A, 113(2), 345–424.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial & Manufacturing Engineering, The Pennsylvania State University, University Park, PA, USA

    Terry L. Friesz

  2. School of Transportation and Logistics, Southwest Jiaotong University, Chengdu, China

    Ke Han

Authors
  1. Terry L. Friesz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ke Han
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Friesz, T.L., Han, K. (2022). The Differential Variational Inequality Formulation of Dynamic User Equilibria. In: Dynamic Network User Equilibrium. Complex Networks and Dynamic Systems, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-031-25564-9_4

Download citation

Publish with us

Policies and ethics

Search

Navigation