Article ID: | iaor20123741 |
Volume: | 153 |
Issue: | 2 |
Start Page Number: | 377 |
End Page Number: | 387 |
Publication Date: | May 2012 |
Journal: | Journal of Optimization Theory and Applications |
Authors: | Dang Chuangyin, Jiang Ming, Meng Zhiqing, Shen Rui |
Keywords: | penalty functions, programming (bilevel) |
Penalty methods are very efficient in finding an optimal solution to constrained optimization problems. In this paper, we present an objective penalty function with two penalty parameters for inequality constrained bilevel programming under the convexity assumption to the lower level problem. Under some conditions, an optimal solution to a bilevel programming defined by the objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the objective penalty function, an algorithm is developed to obtain an optimal solution to the original bilevel programming, with its convergence proved under some conditions.