Exact penalty functions for convex bilevel programming problems

G. S. Liu; J. Y. Han; J. Z. Zhang

doi:10.1023/A:1017592429235

Exact penalty functions for convex bilevel programming problems

G. S. Liu
, J. Y. Han
, J. Z. Zhang

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

34 Citations (Scopus)

Abstract

In this paper, we propose a new constraint qualification for convex bilevel programming problems. Under this constraint qualification, a locally and globally exact penalty function of order 1 for a single-level reformulation of convex bilevel programming problems is given without requiring the linear independence condition and the strict complementarity condition to hold in the lower-level problem. Based on these results, locally and globally exact penalty functions for two other single-level reformulations of convex bilevel programming problems can be obtained. Furthermore, sufficient conditions for partial calmness to hold in some single-level reformulations of convex bilevel programming problems can be given.
© 2001 Plenum Publishing Corporation

Original language	English
Pages (from-to)	621-643
Journal	Journal of Optimization Theory and Applications
Volume	110
Issue number	3
DOIs	https://doi.org/10.1023/A:1017592429235
Publication status	Published - 1 Sept 2001
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

1This research was partially supported by the City University of Hong Kong under Strategic Research Grant 7000866 and the National Natural Science Foundation of China under Grant 19901002.

Research Keywords

Bilevel programming problems
Constraint qualifications
Exact penalty functions
Partial calmness
Reformulations

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title = "Exact penalty functions for convex bilevel programming problems",

abstract = "In this paper, we propose a new constraint qualification for convex bilevel programming problems. Under this constraint qualification, a locally and globally exact penalty function of order 1 for a single-level reformulation of convex bilevel programming problems is given without requiring the linear independence condition and the strict complementarity condition to hold in the lower-level problem. Based on these results, locally and globally exact penalty functions for two other single-level reformulations of convex bilevel programming problems can be obtained. Furthermore, sufficient conditions for partial calmness to hold in some single-level reformulations of convex bilevel programming problems can be given. {\textcopyright} 2001 Plenum Publishing Corporation",

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AU - Liu, G. S.

AU - Han, J. Y.

AU - Zhang, J. Z.

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N2 - In this paper, we propose a new constraint qualification for convex bilevel programming problems. Under this constraint qualification, a locally and globally exact penalty function of order 1 for a single-level reformulation of convex bilevel programming problems is given without requiring the linear independence condition and the strict complementarity condition to hold in the lower-level problem. Based on these results, locally and globally exact penalty functions for two other single-level reformulations of convex bilevel programming problems can be obtained. Furthermore, sufficient conditions for partial calmness to hold in some single-level reformulations of convex bilevel programming problems can be given. © 2001 Plenum Publishing Corporation

AB - In this paper, we propose a new constraint qualification for convex bilevel programming problems. Under this constraint qualification, a locally and globally exact penalty function of order 1 for a single-level reformulation of convex bilevel programming problems is given without requiring the linear independence condition and the strict complementarity condition to hold in the lower-level problem. Based on these results, locally and globally exact penalty functions for two other single-level reformulations of convex bilevel programming problems can be obtained. Furthermore, sufficient conditions for partial calmness to hold in some single-level reformulations of convex bilevel programming problems can be given. © 2001 Plenum Publishing Corporation

KW - Bilevel programming problems

KW - Constraint qualifications

KW - Exact penalty functions

KW - Partial calmness

KW - Reformulations

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DO - 10.1023/A:1017592429235

M3 - RGC 21 - Publication in refereed journal

SN - 0022-3239

VL - 110

SP - 621

EP - 643

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 3

ER -

Exact penalty functions for convex bilevel programming problems

Abstract

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