Descent methods of calculation locally optimal signal controls and prices in multi-modal and dynamic transportation networks

Michael John Smith; Y Xiang; Robert Yarrow

Descent methods of calculation locally optimal signal controls and prices in multi-modal and dynamic transportation networks

Michael John Smith, Y Xiang, Robert Yarrow

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

A bilevel descent method of optimizing signals and prices for a multi-modal network while taking account of travellers' choices (equilibrium) is specified within a framework which may, when developed, be efficient for large networks. Similar trilevel methods for the corresponding dynamic problem are also presented. Fairly complete proofs of convergence of the method to a local optimum are given for the steady state case but there remains a gap when the authors seek to prove convergence in a dynamic context; however, if the method converges (in a dynamic context) to the set of equilibria then (under natural conditions) it must also converge to the set of local optima.

Original language	English
Title of host publication	Transportation Networks: Recent Methodological Advances
Subtitle of host publication	Selected Proceedings of the 4th EURO Transportation Meeting
Publisher	Pergamon
Pages	9-34
ISBN (Print)	008043052X
Publication status	Published - 1998

Cite this

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title = "Descent methods of calculation locally optimal signal controls and prices in multi-modal and dynamic transportation networks",

abstract = "A bilevel descent method of optimizing signals and prices for a multi-modal network while taking account of travellers' choices (equilibrium) is specified within a framework which may, when developed, be efficient for large networks. Similar trilevel methods for the corresponding dynamic problem are also presented. Fairly complete proofs of convergence of the method to a local optimum are given for the steady state case but there remains a gap when the authors seek to prove convergence in a dynamic context; however, if the method converges (in a dynamic context) to the set of equilibria then (under natural conditions) it must also converge to the set of local optima.",

author = "Smith, {Michael John} and Y Xiang and Robert Yarrow",

year = "1998",

language = "English",

isbn = "008043052X ",

pages = "9--34",

booktitle = "Transportation Networks: Recent Methodological Advances",

publisher = "Pergamon",

address = "United Kingdom",

}

Descent methods of calculation locally optimal signal controls and prices in multi-modal and dynamic transportation networks. / Smith, Michael John; Xiang, Y; Yarrow, Robert.
Transportation Networks: Recent Methodological Advances: Selected Proceedings of the 4th EURO Transportation Meeting. Pergamon, 1998. p. 9-34.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Descent methods of calculation locally optimal signal controls and prices in multi-modal and dynamic transportation networks

AU - Smith, Michael John

AU - Xiang, Y

AU - Yarrow, Robert

PY - 1998

Y1 - 1998

N2 - A bilevel descent method of optimizing signals and prices for a multi-modal network while taking account of travellers' choices (equilibrium) is specified within a framework which may, when developed, be efficient for large networks. Similar trilevel methods for the corresponding dynamic problem are also presented. Fairly complete proofs of convergence of the method to a local optimum are given for the steady state case but there remains a gap when the authors seek to prove convergence in a dynamic context; however, if the method converges (in a dynamic context) to the set of equilibria then (under natural conditions) it must also converge to the set of local optima.

AB - A bilevel descent method of optimizing signals and prices for a multi-modal network while taking account of travellers' choices (equilibrium) is specified within a framework which may, when developed, be efficient for large networks. Similar trilevel methods for the corresponding dynamic problem are also presented. Fairly complete proofs of convergence of the method to a local optimum are given for the steady state case but there remains a gap when the authors seek to prove convergence in a dynamic context; however, if the method converges (in a dynamic context) to the set of equilibria then (under natural conditions) it must also converge to the set of local optima.

M3 - Chapter

SN - 008043052X

SP - 9

EP - 34

BT - Transportation Networks: Recent Methodological Advances

PB - Pergamon

ER -