A Class of Collinear Scaling Algorithms for Unconstrained Optimization. An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been in troduced by ...A Class of Collinear Scaling Algorithms for Unconstrained Optimization. An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been in troduced by Davidon (1980). It leads to a broad class of algorithms which can be considered to generalize the existing quasi-Newton methods. One particular member of this class has been deeply discussed by Sorensen (1980), who has proved some interesting theoretical properties. In this paper, we generalize Sorensen’s technique to Spedicato three-parameter family of variable-metric updates. Furthermore, we point out that the collinear scaling three- parameter family is essentially equivalent to the Spedicato three-parameter family. In addition, numerical expriments have been carried out to compare some colliner scaling algorithms with a straightforward implementation of the BFGS quasi-Newton method.展开更多
In this paper, a bi-level formulation of the continuous network design problem (NDP) is proposed on the basis of logit stochastic user equilibrium (SUE) assignment with elastic demand. The model determines the link ca...In this paper, a bi-level formulation of the continuous network design problem (NDP) is proposed on the basis of logit stochastic user equilibrium (SUE) assignment with elastic demand. The model determines the link capacity improvements by maximizing net economic benefit while considering changes in demand and traffic distribution in network. The derivatives of equilibrium link flows and objective function with respect to capacity expansion variables, which are analytically derived, can be computed without having to first find path choice information. These derivatives are employed to develop a quasi Newton algorithm with the BFG S (Broyden- Fletcher- Goldfarb-Shanno) formula for solving the nonlinear, nonconvex but differentiable SUE-constrained network design problem. The SUE assignment with elastic demand is solved by using the method of successive averages in conjunction with Bell’s matrix inversion logit assignment method. Simple and complex example networks are presented to illustrate the model and the algorithm.展开更多
基金Supported by NNSF of China and NSF of Jiangsu Province
文摘A Class of Collinear Scaling Algorithms for Unconstrained Optimization. An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been in troduced by Davidon (1980). It leads to a broad class of algorithms which can be considered to generalize the existing quasi-Newton methods. One particular member of this class has been deeply discussed by Sorensen (1980), who has proved some interesting theoretical properties. In this paper, we generalize Sorensen’s technique to Spedicato three-parameter family of variable-metric updates. Furthermore, we point out that the collinear scaling three- parameter family is essentially equivalent to the Spedicato three-parameter family. In addition, numerical expriments have been carried out to compare some colliner scaling algorithms with a straightforward implementation of the BFGS quasi-Newton method.
基金Huang gratefully acknowledges the National Natural Science Foundation of China(Grant No. 79825001)and the Ministry of Educatio
文摘In this paper, a bi-level formulation of the continuous network design problem (NDP) is proposed on the basis of logit stochastic user equilibrium (SUE) assignment with elastic demand. The model determines the link capacity improvements by maximizing net economic benefit while considering changes in demand and traffic distribution in network. The derivatives of equilibrium link flows and objective function with respect to capacity expansion variables, which are analytically derived, can be computed without having to first find path choice information. These derivatives are employed to develop a quasi Newton algorithm with the BFG S (Broyden- Fletcher- Goldfarb-Shanno) formula for solving the nonlinear, nonconvex but differentiable SUE-constrained network design problem. The SUE assignment with elastic demand is solved by using the method of successive averages in conjunction with Bell’s matrix inversion logit assignment method. Simple and complex example networks are presented to illustrate the model and the algorithm.
