Finding the ε-user Equilibrium Solution Using an Augmented Frank-Wolfe Algorithm

Hsun-Jung Cho*, Yu Kuang Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The Frank-Wolfe algorithm has been extensively adopted in recent decades to solve the user-equilibrium problem because of its simple structure and low memory requirements. However, Dial observed that the results obtained by the Frank-Wolfe algorithm differed markedly from the B algorithm of Dial in terms of link flows, and the results obtained via Frank-Wolfe algorithm could be incorrect. This study attempts to provide a clear example showing that the Frank-Wolfe algorithm has difficulty in achieving an ε-user equilibrium state when ε is sufficiently small. An Augmented Frank-Wolfe algorithm is presented that overcomes the weaknesses of the conventional arc-based Frank-Wolfe algorithm.

Original languageEnglish
Pages (from-to)473-485
Number of pages13
JournalNetworks and Spatial Economics
Issue number4
StatePublished - 1 Dec 2010


  • Frank-Wolfe
  • User-equilibrium

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