A new method for  strong-weak  linear bilevel programming problem

Yue Zheng; Zhongping Wan; Shihui Jia; Guangmin Wang

doi:10.3934/jimo.2015.11.529

Article Contents

2015, Volume 11, Issue 2: 529-547. Doi: 10.3934/jimo.2015.11.529

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A new method for strong-weak linear bilevel programming problem

1.
College of Mathematics and Physics, Huanggang Normal University, Huanggang 438000
2.
School of Mathematics and Statistics, Wuhan University, Wuhan, 430072
3.
School of Science, Wuhan University of Science and Technology, Wuhan 430081
4.
School of Economics and Management, China University of Geosciences, Wuhan 430074

Received: September 30, 2012

Revised: March 31, 2014

Published: March 2015

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Abstract

We first propose an exact penalty method to solve strong-weak linear bilevel programming problem (for short, SWLBP) for every fixed cooperation degree from the follower. Then, we prove that the solution of penalized problem is also that of the original problem under some conditions. Furthermore, we give some properties of the optimal value function (as a function of the follower's cooperation degree) of SWLBP. Finally, we develop a method to acquire the critical points of the optimal value function without enumerating all values of the cooperation degree from the follower, and thus this function is also achieved. Numerical results show that the proposed methods are feasible.

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Mathematics Subject Classification: Primary: 90C26, 90C30.

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