Exact Penalization and Necessary Optimality Conditions for Generalized Bilevel Programming Problems

Authors

J. J. Ye, University of Victoria
D. L. Zhu, Shanghai Jiaotong University
Qiji Jim Zhu, Western Michigan UniversityFollow

Document Type

Article

Publication Date

1997

Abstract

The generalized bilevel programming problem (GBLP) is a bilevel mathematical program where the lower level is a variational inequality. In this paper we prove that if the objective function of a GBLP is uniformly Lipschitz continuous in the lower level decision variable with respect to the upper level decision variable, then using certain uniform parametric error bounds as penalty functions gives single level problems equivalent to the GBLP. Several local and global uniform parametric error bounds are presented, and assumptions guaranteeing that they apply are discussed. We then derive Kuhn--Tucker-type necessary optimality conditions by using exact penalty formulations and nonsmooth analysis.

Comments

https://doi.org/10.1137/S1052623493257344

WMU ScholarWorks Citation

Ye, J. J.; Zhu, D. L.; and Zhu, Qiji Jim, "Exact Penalization and Necessary Optimality Conditions for Generalized Bilevel Programming Problems" (1997). Math Faculty Publications. 8.
https://scholarworks.wmich.edu/math_pubs/8