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.
447-473
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e
1 April 2013
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), .
(doi:10.1007/s10107-011-0508-5).
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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Published date: 1 April 2013
Organisations:
Operational Research
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Local EPrints ID: 370839
URI: http://eprints.soton.ac.uk/id/eprint/370839
ISSN: 0025-5610
PURE UUID: b3342067-6004-4ad6-aa0d-747722d46f16
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Date deposited: 10 Nov 2014 13:25
Last modified: 15 Mar 2024 03:51
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Author:
Stephan Dempe
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