A Trust Region Algorithm for Solving Bilevel Programming Problems

作     者：Guo-shan LIU Shi-qin XU Ji-ye HAN 

作者机构：School of BusinessRenmin University of China Academy of Mathematics and Systems ScienceChinese Academy of Sciences 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2013年第29卷第3期

页      面：491-498页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(No.11171348 11171252 and 71232011) 

主　　题：Bilevel programming problem trust region algorithm global convergence mathematical program with equilibrium constraints stationary point 

摘      要：In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming problem in which the lower level programming problem is a strongly convex programming problem with linear constraints, we show that each accumulation point of the iterative sequence produced by this algorithm is a stationary point of the bilevel programming problem.