On the Karush–Kuhn–Tucker reformulation of the bilevel optimization problem
On the Karush–Kuhn–Tucker reformulation of the bilevel optimization problem
This paper is mainly concerned with the classical KKT reformulation and the primal KKT reformulation (also known as an optimization problem with generalized equation constraint (OPEC)) of the optimistic bilevel optimization problem. A generalization of the MFCQ to an optimization problem with operator constraint is applied to each of these reformulations, hence leading to new constraint qualifications (CQs) for the bilevel optimization problem. M- and S-type stationarity conditions tailored for the problem are derived as well. Considering the close link between the aforementioned reformulations, similarities and relationships between the corresponding CQs and optimality conditions are highlighted. In this paper, a concept of partial calmness known for the optimal value reformulation is also introduced for the primal KKT reformulation and used to recover the M-stationarity conditions.
1202-1218
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e
February 2012
Dempe, Stephan
a8716b3e-ae75-4998-a6b6-48a9171b925a
Zemkoho, Alain B.
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Dempe, Stephan and Zemkoho, Alain B.
(2012)
On the Karush–Kuhn–Tucker reformulation of the bilevel optimization problem.
Nonlinear Analysis Theory Methods & Applications, 75 (3), .
(doi:10.1016/j.na.2011.05.097).
Abstract
This paper is mainly concerned with the classical KKT reformulation and the primal KKT reformulation (also known as an optimization problem with generalized equation constraint (OPEC)) of the optimistic bilevel optimization problem. A generalization of the MFCQ to an optimization problem with operator constraint is applied to each of these reformulations, hence leading to new constraint qualifications (CQs) for the bilevel optimization problem. M- and S-type stationarity conditions tailored for the problem are derived as well. Considering the close link between the aforementioned reformulations, similarities and relationships between the corresponding CQs and optimality conditions are highlighted. In this paper, a concept of partial calmness known for the optimal value reformulation is also introduced for the primal KKT reformulation and used to recover the M-stationarity conditions.
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Published date: February 2012
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Operational Research
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Local EPrints ID: 370842
URI: http://eprints.soton.ac.uk/id/eprint/370842
ISSN: 0362-546X
PURE UUID: 81c45311-71b7-4178-ada0-54838da97a01
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Date deposited: 10 Nov 2014 13:30
Last modified: 15 Mar 2024 03:51
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Stephan Dempe
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