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Two level value function approach to nonsmooth optimistic and pessimistic bilevel programs

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
0233-1934
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
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), 433-455. (doi:10.1080/02331934.2018.1543294).

Record type: Article

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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More information

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
ORCID for Alain B. Zemkoho: ORCID iD orcid.org/0000-0003-1265-4178

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Date deposited: 06 Dec 2017 17:30
Last modified: 15 Nov 2019 05:01

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