IJPAM: Volume 18, No. 4 (2005)

THE SOLUTION CONCEPTS AND THE OPTIMALITY
CONDITION FOR A KIND OF BILEVEL
PROGRAMMING WITH MULTIFOLLOWERS

Lili Han$^1$, Rongsheng Li$^2$
$^{1,2}$Institute of Operation Research
Qufu Normal University
Rizhao, Shandong, 276826, P.R. CHINA
$^1$e-mail: hllsd@eyou.edu.cn
$^2$e-mail: lrs@qrnu.edu.cn


Abstract.In this paper, we introduce some new solution concepts for a bilevel programming problem with multiple followers based on the Pareto solution of multi-objective programming. We discuss the relation between the new solutions and the existing solutions and we give the optimality condition for a kind bilevel programming with multiple followers based on which, we can solve a class of bilevel programming with multiple followers via solving a corresponding bilevel programming with a single follower.

Received: December 12, 2004

AMS Subject Classification: 90C30, 90C90

Key Words and Phrases: bilevel programming, Stackelberg decision, Pareto solution

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 18
Issue: 4