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Exact Penalty Functions for Convex Bilevel Programming Problems

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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.

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Authors
  1. G. S. Liu
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  2. J. Y. Han
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  3. J. Z. Zhang
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Liu, G.S., Han, J.Y. & Zhang, J.Z. Exact Penalty Functions for Convex Bilevel Programming Problems. Journal of Optimization Theory and Applications 110, 621–643 (2001). https://doi.org/10.1023/A:1017592429235

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