A truncated Newton method with nonmonotone line search for unconstrained optimization

1989 ◽  
Vol 60 (3) ◽  
pp. 401-419 ◽  
Author(s):  
L. Grippo ◽  
F. Lampariello ◽  
S. Lucidi
Keyword(s):  
Unconstrained Optimization ◽  
Newton Method ◽  
Line Search ◽  
Nonmonotone Line Search ◽  
Truncated Newton Method ◽  
Truncated Newton

scholarly journals Improving Truncated Newton Method for the Logit-Based Stochastic User Equilibrium Problem

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Min Xu ◽  
Bojian Zhou ◽  
Jie He
Keyword(s):  
Equilibrium Problem ◽  
Newton Method ◽  
Computational Efficiency ◽  
Initial Point ◽  
User Equilibrium ◽  
Point Of View ◽  
Theoretical Point ◽  
Stochastic User Equilibrium ◽  
Truncated Newton Method ◽  
Truncated Newton

This study proposes an improved truncated Newton (ITN) method for the logit-based stochastic user equilibrium problem. The ITN method incorporates a preprocessing procedure to the traditional truncated Newton method so that a good initial point is generated, on the basis of which a useful principle is developed for the choice of the basic variables. We discuss the rationale of both improvements from a theoretical point of view and demonstrate that they can enhance the computational efficiency in the early and late iteration stages, respectively, when solving the logit-based stochastic user equilibrium problem. The ITN method is compared with other related methods in the literature. Numerical results show that the ITN method performs favorably over these methods.

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