Title :
The basic properties and algorithm of a linear bilevel programming model with multiple followers
Author :
Shengyue Deng ; Yangjin Cheng ; Xinfan Wang
Author_Institution :
Sch. of Sci., Hunan Univ. of Technol., Zhuzhou, China
fDate :
May 31 2014-June 2 2014
Abstract :
The geometric properties and optimality conditions for a class of typical model of linear bilevel programming with multiple followers are discussed in this paper. Under the assumption that the constrained set is nonempty and bounded, we study the geometric properties of the feasible set and reach the conclusion of the feasible set of weak quasi-convex and connected set. An optimum condition is obtained by using the duality theory of linear programming. According to these properties, an algorithm is proposed to solve the model and to verify the correctness of the theory and the feasibility of algorithm by giving the examples of numerical calculation.
Keywords :
convex programming; duality (mathematics); linear programming; set theory; connected set; constrained set; duality theory; feasible set; geometric properties; linear bilevel programming model; linear programming; optimality conditions; quasiconvex set; Computational modeling; Educational institutions; Linear programming; Numerical models; Programming profession; Vectors; bilevel linear programming; geometric property; multiple followers; optimum condition;
Conference_Titel :
Control and Decision Conference (2014 CCDC), The 26th Chinese
Conference_Location :
Changsha
Print_ISBN :
978-1-4799-3707-3
DOI :
10.1109/CCDC.2014.6852309
