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The bilevel programming problem: reformulations, constraint qualifications and optimality conditions

The bilevel programming problem: reformulations, constraint qualifications and optimality conditions
The bilevel programming problem: reformulations, constraint qualifications and optimality conditions
We consider the bilevel programming problem and its optimal value and KKT one level reformulations. The two reformulations are studied in a unified manner and compared in terms of optimal solutions, constraint qualifications and optimality conditions. We also show that any bilevel programming problem where the lower level problem is linear with respect to the lower level variable, is partially calm without any restrictive assumption. Finally, we consider the bilevel demand adjustment problem in transportation, and show how KKT type optimality conditions can be obtained under the partial calmness, using the differential calculus of Mordukhovich.
0025-5610
447-473
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e

Dempe, Stephan and Zemkoho, Alain B. (2013) The bilevel programming problem: reformulations, constraint qualifications and optimality conditions. Mathematical Programming, 138 (1-2), 447-473. (doi:10.1007/s10107-011-0508-5).

Record type: Article

Abstract

We consider the bilevel programming problem and its optimal value and KKT one level reformulations. The two reformulations are studied in a unified manner and compared in terms of optimal solutions, constraint qualifications and optimality conditions. We also show that any bilevel programming problem where the lower level problem is linear with respect to the lower level variable, is partially calm without any restrictive assumption. Finally, we consider the bilevel demand adjustment problem in transportation, and show how KKT type optimality conditions can be obtained under the partial calmness, using the differential calculus of Mordukhovich.

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More information

Published date: 1 April 2013
Organisations: Operational Research

Identifiers

Local EPrints ID: 370839
URI: http://eprints.soton.ac.uk/id/eprint/370839
ISSN: 0025-5610
PURE UUID: b3342067-6004-4ad6-aa0d-747722d46f16
ORCID for Alain B. Zemkoho: ORCID iD orcid.org/0000-0003-1265-4178

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Date deposited: 10 Nov 2014 13:25
Last modified: 10 Jan 2022 03:03

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Author: Stephan Dempe

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