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New optimality conditions for the semivectorial bilevel optimization problem

New optimality conditions for the semivectorial bilevel optimization problem
New optimality conditions for the semivectorial bilevel optimization problem
The paper is concerned with the optimistic formulation of a bilevel optimization problem with multiobjective lower-level problem. Considering the scalarization approach for the multiobjective program, we transform our problem into a scalar-objective optimization problem with inequality constraints by means of the well-known optimal value reformulation. Completely detailed first-order necessary optimality conditions are then derived in the smooth and nonsmooth settings while using the generalized differentiation calculus of Mordukhovich. Our approach is different from the one previously used in the literature and the conditions obtained are new. Furthermore, they reduce to those of a usual bilevel program, if the lower-level objective function becomes single-valued.
semivectorial bilevel optimization, multiobjective optimization, weakly efficient solution, optimal value function, optimality conditions
0022-3239
54-74
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Gadhi, Nazih
956ea8de-8742-4e77-a6a7-977b4f5fa77a
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Gadhi, Nazih
956ea8de-8742-4e77-a6a7-977b4f5fa77a
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e

Dempe, Stephan, Gadhi, Nazih and Zemkoho, Alain B. (2013) New optimality conditions for the semivectorial bilevel optimization problem. Journal of Optimization Theory and Applications, 157 (1), 54-74. (doi:10.1007/s10957-012-0161-z).

Record type: Article

Abstract

The paper is concerned with the optimistic formulation of a bilevel optimization problem with multiobjective lower-level problem. Considering the scalarization approach for the multiobjective program, we transform our problem into a scalar-objective optimization problem with inequality constraints by means of the well-known optimal value reformulation. Completely detailed first-order necessary optimality conditions are then derived in the smooth and nonsmooth settings while using the generalized differentiation calculus of Mordukhovich. Our approach is different from the one previously used in the literature and the conditions obtained are new. Furthermore, they reduce to those of a usual bilevel program, if the lower-level objective function becomes single-valued.

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More information

e-pub ahead of print date: 30 August 2012
Published date: April 2013
Keywords: semivectorial bilevel optimization, multiobjective optimization, weakly efficient solution, optimal value function, optimality conditions
Organisations: Operational Research

Identifiers

Local EPrints ID: 370840
URI: http://eprints.soton.ac.uk/id/eprint/370840
ISSN: 0022-3239
PURE UUID: a7798407-8c30-4313-92d9-866c19a987d2
ORCID for Alain B. Zemkoho: ORCID iD orcid.org/0000-0003-1265-4178

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Date deposited: 10 Nov 2014 13:35
Last modified: 28 Apr 2022 02:12

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Contributors

Author: Stephan Dempe
Author: Nazih Gadhi

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