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A Trust Region Algorithm for Solving Bilevel Programming Problems

A Trust Region Algorithm for Solving Bilevel Programming Problems
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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. 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.
作者 Guo-shan LIU Shi-qin XU Ji-ye HAN
机构地区 School of Business Academy of Mathematics and Systems Science
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2013年第3期491-498,共8页 应用数学学报（英文版）
基金 Supported by the National Natural Science Foundation of China(No.11171348,11171252 and 71232011)
关键词 Bilevel programming problem trust region algorithm global convergence mathematical program with equilibrium constraints stationary point Bilevel programming problem trust region algorithm global convergence mathematical program with equilibrium constraints stationary point
分类号 O221 [理学—运筹学与控制论]
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Acta Mathematicae Applicatae Sinica
2013年 第3期

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