JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE) ›› 2018, Vol. 48 ›› Issue (1): 36-41.doi: 10.6040/j.issn.1672-3961.0.2016.408

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A modified truncated quasi-Newton method based on BFGS formula for the stochastic user equilibrium problem

LIU Jianmei, MA Shuaiqi*   

  1. Department of Mathematics, Jining University, Jining 273155, Shandong, China
  • Received:2016-11-07 Online:2018-02-20 Published:2016-11-07

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Abstract: According to the characteristics of stochastic user equilibrium problems, a modified truncated quasi-Newton(MTQN)method was constructed based on the BFGS correction formula and Armijo line search. The construction process of truncated quasi-Newton equation and the concrete steps of the MTQN algorithm were introduced. The convergence and two issues were presented for the characteristics of stochastic user equilibrium model. One numerical example was solved by the MTQN algorithm, and the results were compared with the modified truncated Newton(MTN)method, which showed that the MTQN was superior to the MTN in both iteration number and absolute error. The modified truncated quasi-Newton method could avoid the computation of the Hessian matrix and could be also applied to solve some special problems when the Hessian matrix was not positive definite.

Key words: BFGS formula, truncated quasi-Newton method, Armijo condition, condition number, stochastic user equilibrium

CLC Number: 

  • U491
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