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A trust region algorithm for solving bilevel programming problems

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Abstract

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.

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Authors and Affiliations

  1. School of Business, Renmin University of China, Beijing, 100872, China

    Guo-shan Liu & Shi-qin Xu

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Ji-ye Han

Authors
  1. Guo-shan Liu
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  2. Shi-qin Xu
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  3. Ji-ye Han
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Corresponding authors

Correspondence to Guo-shan Liu or Shi-qin Xu.

Additional information

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

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Liu, Gs., Xu, Sq. & Han, Jy. A trust region algorithm for solving bilevel programming problems. Acta Math. Appl. Sin. Engl. Ser. 29, 491–498 (2013). https://doi.org/10.1007/s10255-013-0231-5

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  • DOI: https://doi.org/10.1007/s10255-013-0231-5

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