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: | Marcotte P., Zhu D. L. |
Keywords: | bilevel optimization, penalty functions |
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.