An Objective Penalty Function Algorithm for Bilevel Programming Based on Multi-Parameters

Abstract

In this article, an objective penalty function algorithm based on multi-parameters is proposed for solving bilevel programming convex to the lower level problem. Under some conditions, an optimal solution to a single-objective programming defined by the objective penalty function is proved to be an optimal solution to the original bilevel programming. We prove that the algorithm is convergent under some conditions. Numerical results show that the algorithm is efficient for solving some bilevel programming convex to the lower level problem.

Keywords:

• Bilevel programming
• Convexity
• Objective penalty function
• Smoothing

Mathematics Subject Classification:

• Primary 65K05
• Secondary 90C30

ACKNOWLEDGMENTS

This work is supported by the National Natural Science Foundation of China (10971193), the Natural Science Foundation of Zhejiang Province (Y6090063), the Natural Science Foundation of Shandong Province (ZR2010AM029), and the Science Foundation of Binzhou University(BZXYL1009, BZXYQNLG201009).

The authors would like to express their gratitude to anonymous referees’ detailed comments and remarks that help us improve our presentation of this article considerably.