Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities

He, Bing; Liao, Li-Zhi

doi:10.1023/a:1013096613105

Cited by 203 publications

(97 citation statements)

References 19 publications

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“…In this section, we adopt the self-adaptive predictor-corrector (PC) method proposed by He and Liao [43], which is an extension of the PC method with advanced self-adaptive step sizes. We see that this method can converge linearly, which is efficient for practical implementations.…”

Section: Trial-and-error Methodsmentioning

confidence: 99%

A Trial-and-Error Method with Autonomous Vehicle-to-Infrastructure Traffic Counts for Cordon-Based Congestion Pricing

Liu

Zhang

Wang

et al. 2017

Journal of Advanced Transportation

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This study proposes a practical trial-and-error method to solve the optimal toll design problem of cordon-based pricing, where only the traffic counts autonomously collected on the entry links of the pricing cordon are needed. With the fast development and adoption of vehicle-to-infrastructure (V2I) facilities, it is very convenient to autonomously collect these data. Two practical properties of the cordon-based pricing are further considered in this article: the toll charge on each entry of one pricing cordon is identical; the total inbound flow to one cordon should be restricted in order to maintain the traffic conditions within the cordon area. Then, the stochastic user equilibrium (SUE) with asymmetric link travel time functions is used to assess each feasible toll pattern. Based on a variational inequality (VI) model for the optimal toll pattern, this study proposes a theoretically convergent trial-and-error method for the addressed problem, where only traffic counts data are needed. Finally, the proposed method is verified based on a numerical network example.

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Section: Trial-and-error Methodsmentioning

confidence: 99%

A Trial-and-Error Method with Autonomous Vehicle-to-Infrastructure Traffic Counts for Cordon-Based Congestion Pricing

Liu

Zhang

Wang

et al. 2017

Journal of Advanced Transportation

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“…the direction where satisfies similarly as (6.13) but is not restricted to a given set, in He and Liao (2002); the classical direction as in Goldstein (1964), Levitin et al (1966), Sibony (1970) and Noor (2003c); the direction in He (1997).…”

Section: Is (By (9)) or (By (12)) For The Sake Of Comparison We Givmentioning

confidence: 99%

A Projection-Type Algorithm for Pseudomonotone Nonlipschitzian Multivalued Variational Inequalities

Bao

Khánh

Generalized Convexity, Generalized Monotonicity and Applications

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We propose a projection-type algorithm for variational inequalities involving multifunction. The algorithm requires two projections on the constraint set only in a part of iterations (one third of the subcases). For the other iterations, only one projection is used. A global convergence is proved under the weak assumption that the multifunction of the problem is pseudomonotone at a solution, closed, lower hemicontinuous, and bounded on each bounded subset (it is not necessarily continuous). Some numerical test problems are implemented by using MATLAB with encouraging effectiveness.

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“…as the whole non-negative orthant, the conditions (9)- (11) are equivalent to the following VI model (He and Liao, 2002):…”

Section: Variational Inequality (Vi) Model For the Optimal Lagrangianmentioning

confidence: 99%

“…A theoretically more efficient method is the self-adaptive PC method proposed by He and Liao (2002), which is an extension of the PC method with advanced self-adaptive step sizes. The self-adaptive PC method maintains a linear convergent speed.…”

Section: Variational Inequality (Vi) Model For the Optimal Lagrangianmentioning

confidence: 99%

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Variational inequality model for cordon-based congestion pricing under side constrained stochastic user equilibrium conditions

Liu

Meng

Wang

2013

Transportmetrica A: Transport Science

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A major objective of the practical implemented cordon-based congestion pricing schemes is to maintain the traffic conditions within the cordon area, which is rarely considered in most of the existing studies. Thus, this paper addresses the optimal toll charge pattern that can restrict the total inbound flow of each cordon to a predetermined threshold. The toll charges on all the entry links of one cordon are required to be identical, for the ease of implementation and users' recognition. The users' route choice behaviour is assumed to follow stochastic user equilibrium (SUE) with asymmetric link travel time functions. It is shown that such an optimal toll charge pattern can be attained by solving a SUE problem with side constraints.A variational inequality (VI) model is first proposed for the optimal toll pattern, where the monotone property of this model is rigorously proved. Then, a convergent self-adaptive prediction and correction method can be adopted for solving the VI model. It is shown that when used in practice, the solution method only needs traffic counts on entry links of each cordon. ABSTRACTA major objective of the practical implemented cordon-based congestion pricing schemes is to maintain the traffic conditions within the cordon area, which is rarely considered in most of the existing studies. Thus, this paper addresses the optimal toll charge pattern that can restrict the total inbound flow of each cordon to a predetermined threshold. The toll charges on all the entry links of one cordon are required to be identical, for the ease of implementation and users' recognition. The users' route choice behavior is assumed to follow stochastic user equilibrium (SUE) with asymmetric link travel time functions. It is shown that such an optimal toll charge pattern can be attained by solving a SUE problem with side constraints. A variational inequality (VI) model is first proposed for the optimal toll pattern, where the monotone property of this model is rigorously proven. Then, a convergent self-adaptive prediction and correction method can be adopted for solving the VI model. It is shown that when used in practice, the solution method only needs traffic counts on entry links of each cordon.

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Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities

Cited by 203 publications

References 19 publications

A Trial-and-Error Method with Autonomous Vehicle-to-Infrastructure Traffic Counts for Cordon-Based Congestion Pricing

A Trial-and-Error Method with Autonomous Vehicle-to-Infrastructure Traffic Counts for Cordon-Based Congestion Pricing

A Projection-Type Algorithm for Pseudomonotone Nonlipschitzian Multivalued Variational Inequalities

Variational inequality model for cordon-based congestion pricing under side constrained stochastic user equilibrium conditions

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