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Mathematics > Optimization and Control

arXiv:2205.10944 (math)
[Submitted on 22 May 2022]

Title:Duality theory for optimistic bilevel optimization

Authors:Houria En-Naciri, Lahoussine Lafhim, Alain Zemkoho
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Abstract:In this paper, we exploit the so-called value function reformulation of the bilevel optimization problem to develop duality results for the problem. Our approach builds on Fenchel-Lagrange-type duality to establish suitable results for the bilevel optimization problem. First, we overview some standard duality results to show that they are not applicable to our problem. Secondly, via the concept of partial calmness, we establish weak and strong duality results. In particular, Lagrange, Fenchel-Lagrange, and Toland-Fenchel- Lagrange duality concepts are investigated for this type of problems under some suitable conditions. Thirdly, based on the use of some regularization of our bilevel program, we establish sufficient conditions ensuring strong duality results under a generalized Slater-type condition without convexity assumptions and without the partial calmness condition. Finally, without the Slater condition, a strong duality result is constructed for the bilevel optimization problem with geometric constraint.
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:2205.10944 [math.OC]
  (or arXiv:2205.10944v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2205.10944

Submission history

From: Alain Zemkoho [view email]
[v1] Sun, 22 May 2022 22:42:16 UTC (21 KB)
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