Bilevel road pricing: theoretical analysis and optimality conditions
Bilevel road pricing: theoretical analysis and optimality conditions
We consider the bilevel road pricing problem. In contrary to the Karush-Kuhn-Tucker (one level) reformulation, the optimal value reformulation is globally and locally equivalent to the initial problem. Moreover, in the process of deriving optimality conditions, the optimal value reformulation helps to preserve some essential data involved in the traffic assignment problem that may disappear with the Karush-Kuhn-Tucker (KKT) one. Hence, we consider in this work the optimal value reformulation of the bilevel road pricing problem; using some recent developments in nonsmooth analysis, we derive implementable KKT type optimality conditions for the problem containing all the necessary information. The issue of estimating the (fixed) demand required for the road pricing problem is a quite difficult problem which has been also addressed in recent years using bilevel programming. We also show how the ideas used in designing KKT type optimality conditions for the road pricing problem can be applied to derive optimality conditions for the origin-destination (O-D) matrix estimation problem. Many other theoretical aspects of the bilevel road pricing and O-D matrix estimation problems are also studied in this paper.
bilevel programming, road pricing, o-d matrix estimation, optimal value function, constraint qualifications, optimality conditions
223-240
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e
July 2012
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Dempe, Stephan and Zemkoho, Alain B.
(2012)
Bilevel road pricing: theoretical analysis and optimality conditions.
Annals of Operations Research, 196 (1), .
(doi:10.1007/s10479-011-1023-z).
Abstract
We consider the bilevel road pricing problem. In contrary to the Karush-Kuhn-Tucker (one level) reformulation, the optimal value reformulation is globally and locally equivalent to the initial problem. Moreover, in the process of deriving optimality conditions, the optimal value reformulation helps to preserve some essential data involved in the traffic assignment problem that may disappear with the Karush-Kuhn-Tucker (KKT) one. Hence, we consider in this work the optimal value reformulation of the bilevel road pricing problem; using some recent developments in nonsmooth analysis, we derive implementable KKT type optimality conditions for the problem containing all the necessary information. The issue of estimating the (fixed) demand required for the road pricing problem is a quite difficult problem which has been also addressed in recent years using bilevel programming. We also show how the ideas used in designing KKT type optimality conditions for the road pricing problem can be applied to derive optimality conditions for the origin-destination (O-D) matrix estimation problem. Many other theoretical aspects of the bilevel road pricing and O-D matrix estimation problems are also studied in this paper.
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e-pub ahead of print date: 16 November 2011
Published date: July 2012
Keywords:
bilevel programming, road pricing, o-d matrix estimation, optimal value function, constraint qualifications, optimality conditions
Organisations:
Operational Research
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Local EPrints ID: 370843
URI: http://eprints.soton.ac.uk/id/eprint/370843
PURE UUID: 446b24a5-6610-4943-b94f-3a3419780bf3
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Date deposited: 10 Nov 2014 13:21
Last modified: 15 Mar 2024 03:51
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Author:
Stephan Dempe
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