Necessary optimality conditions in pessimistic bilevel programming
Necessary optimality conditions in pessimistic bilevel programming
This article is devoted to the so-called pessimistic version of bilevel programming programs. Minimization problems of this type are challenging to handle partly because the corresponding value functions are often merely upper (while not lower) semicontinuous. Employing advanced tools of variational analysis and generalized differentiation, we provide rather general frameworks ensuring the Lipschitz continuity of the corresponding value functions. Several types of lower subdifferential necessary optimality conditions are then derived by using the lower-level value function approach and the Karush–Kuhn–Tucker representation of lower-level optimal solution maps. We also derive upper subdifferential necessary optimality conditions of a new type, which can be essentially stronger than the lower ones in some particular settings. Finally, certain links are established between the obtained necessary optimality conditions for the pessimistic and optimistic versions in bilevel programming.
optimization and variational analysis, pessimistic bilevel programs, two-level value functions, sensitivity analysis, generalized differentiation, optimality conditions
505-533
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Mordukhovich, Boris S.
34e6e756-ab21-4760-a6db-fb1f1c94fd93
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e
2014
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Mordukhovich, Boris S.
34e6e756-ab21-4760-a6db-fb1f1c94fd93
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Dempe, Stephan, Mordukhovich, Boris S. and Zemkoho, Alain B.
(2014)
Necessary optimality conditions in pessimistic bilevel programming.
Optimization, 63 (4), .
(doi:10.1080/02331934.2012.696641).
Abstract
This article is devoted to the so-called pessimistic version of bilevel programming programs. Minimization problems of this type are challenging to handle partly because the corresponding value functions are often merely upper (while not lower) semicontinuous. Employing advanced tools of variational analysis and generalized differentiation, we provide rather general frameworks ensuring the Lipschitz continuity of the corresponding value functions. Several types of lower subdifferential necessary optimality conditions are then derived by using the lower-level value function approach and the Karush–Kuhn–Tucker representation of lower-level optimal solution maps. We also derive upper subdifferential necessary optimality conditions of a new type, which can be essentially stronger than the lower ones in some particular settings. Finally, certain links are established between the obtained necessary optimality conditions for the pessimistic and optimistic versions in bilevel programming.
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More information
Accepted/In Press date: 16 May 2012
e-pub ahead of print date: 26 June 2012
Published date: 2014
Keywords:
optimization and variational analysis, pessimistic bilevel programs, two-level value functions, sensitivity analysis, generalized differentiation, optimality conditions
Organisations:
Operational Research
Identifiers
Local EPrints ID: 370837
URI: http://eprints.soton.ac.uk/id/eprint/370837
ISSN: 0233-1934
PURE UUID: 2f971116-d9f5-41b8-bbc3-e47ec0668c42
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Date deposited: 10 Nov 2014 13:16
Last modified: 15 Mar 2024 03:51
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Contributors
Author:
Stephan Dempe
Author:
Boris S. Mordukhovich
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