Two level value function approach to nonsmooth optimistic and pessimistic bilevel programs
Two level value function approach to nonsmooth optimistic and pessimistic bilevel programs
The authors' paper in Optimization 63 (2014), 505533, see Ref. [5], was the rstone to provide detailed optimality conditions for pessimistic bilevel optimization. The results there were based on the concept of the two-level optimal value function introduced and analyzed in SIAM J. Optim. 22 (2012), 13091343; see Ref. [4], for the case of optimistic bilevel programs. One of the basic assumptions in both of these papers is that the functionsinvolved in the problems are at least continuously differentiable. Motivated by the fact that many real-world applications of optimization involve functions that are nondifferentiable at some points of their domain, the main goal of the current paper is extending the two-level value function approach to deriving new necessary optimality conditions for both optimistic and pessimistic versions in bilevel programming with nonsmooth data.
optimistic and pessimistic bilevel programming, two-level value functions, variational analysis, generalized differentiation, optimality conditions
433-455
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Mordukhovich, Boris S.
34e6e756-ab21-4760-a6db-fb1f1c94fd93
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e
15 April 2019
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.
(2019)
Two level value function approach to nonsmooth optimistic and pessimistic bilevel programs.
Optimization, 68 (2-3), .
(doi:10.1080/02331934.2018.1543294).
Abstract
The authors' paper in Optimization 63 (2014), 505533, see Ref. [5], was the rstone to provide detailed optimality conditions for pessimistic bilevel optimization. The results there were based on the concept of the two-level optimal value function introduced and analyzed in SIAM J. Optim. 22 (2012), 13091343; see Ref. [4], for the case of optimistic bilevel programs. One of the basic assumptions in both of these papers is that the functionsinvolved in the problems are at least continuously differentiable. Motivated by the fact that many real-world applications of optimization involve functions that are nondifferentiable at some points of their domain, the main goal of the current paper is extending the two-level value function approach to deriving new necessary optimality conditions for both optimistic and pessimistic versions in bilevel programming with nonsmooth data.
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DemMorZem2017
- Author's Original
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Optimal Value 1118
- Accepted Manuscript
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Accepted/In Press date: 24 October 2018
e-pub ahead of print date: 15 November 2018
Published date: 15 April 2019
Keywords:
optimistic and pessimistic bilevel programming, two-level value functions, variational analysis, generalized differentiation, optimality conditions
Identifiers
Local EPrints ID: 416180
URI: http://eprints.soton.ac.uk/id/eprint/416180
ISSN: 0233-1934
PURE UUID: dea1c037-74e1-4acd-b909-99049485bdb8
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Date deposited: 06 Dec 2017 17:30
Last modified: 16 Mar 2024 05:59
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Author:
Stephan Dempe
Author:
Boris S. Mordukhovich
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