Exact and inexact penalty methods for the generalized bilevel programming problem

Exact and inexact penalty methods for the generalized bilevel programming problem

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Article ID: iaor1998431
Country: Netherlands
Volume: 74
Issue: 2
Start Page Number: 141
End Page Number: 157
Publication Date: Aug 1996
Journal: Mathematical Programming
Authors: ,
Keywords: bilevel optimization, penalty functions
Abstract:

We consider a hierarchical system where a leader incorporates into its strategy the reaction of the follower to its decision. The follower’s reaction is quite generally represented as the solution set to a monotone variational inequality. For the solution of this nonconvex mathematical program a penalty approach is proposed, based on the formulation of the lower level variational inequality as a mathematical program. Under natural regularity conditions, we prove the exactness of a certain penalty function, and give strong necessary optimality conditions for a class of generalized bilevel programs.

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