Exact Penalty Functions for Convex Bilevel Programming Problems

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

Journal of Optimization Theory and Applications, 2001, vol. 110, issue 3, No 8, 643 pages

Abstract: 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.

Keywords: Bilevel programming problems; constraint qualifications; exact penalty functions; reformulations; partial calmness (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (3)

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DOI: 10.1023/A:1017592429235

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