The generalized Mangasarian-Fromowitz constraint qualification and optimality conditions for bilevel programs
The generalized Mangasarian-Fromowitz constraint qualification and optimality conditions for bilevel programs
We consider the optimal value reformulation of the bilevel programming problem. It is shown that the Mangasarian-Fromowitz constraint qualification in terms of the basic generalized differentiation constructions of Mordukhovich, which is weaker than the one in terms of Clarke’s nonsmooth tools, fails without any restrictive assumption. Some weakened forms of this constraint qualification are then suggested, in order to derive Karush-Kuhn-Tucker type optimality conditions for the aforementioned problem. Considering the partial calmness, a new characterization is suggested and the link with the previous constraint qualifications is analyzed.
46-68
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e
1 January 2011
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Dempe, Stephan and Zemkoho, Alain B.
(2011)
The generalized Mangasarian-Fromowitz constraint qualification and optimality conditions for bilevel programs.
Journal of Optimization Theory and Applications, 148 (1), .
(doi:10.1007/s10957-010-9744-8).
Abstract
We consider the optimal value reformulation of the bilevel programming problem. It is shown that the Mangasarian-Fromowitz constraint qualification in terms of the basic generalized differentiation constructions of Mordukhovich, which is weaker than the one in terms of Clarke’s nonsmooth tools, fails without any restrictive assumption. Some weakened forms of this constraint qualification are then suggested, in order to derive Karush-Kuhn-Tucker type optimality conditions for the aforementioned problem. Considering the partial calmness, a new characterization is suggested and the link with the previous constraint qualifications is analyzed.
Text
DZ-GMCQ-2011.pdf
- Other
More information
Published date: 1 January 2011
Organisations:
Operational Research
Identifiers
Local EPrints ID: 370844
URI: http://eprints.soton.ac.uk/id/eprint/370844
ISSN: 0022-3239
PURE UUID: 4489beb4-40cb-4ef8-bce4-03bff62d93c5
Catalogue record
Date deposited: 10 Nov 2014 13:32
Last modified: 15 Mar 2024 03:51
Export record
Altmetrics
Contributors
Author:
Stephan Dempe
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
