Journal of Systems Science and Complexity

, Volume 28, Issue 5, pp 1128–1147 | Cite as

An active-set projected trust region algorithm for box constrained optimization problems

  • Gonglin YuanEmail author
  • Zengxin Wei
  • Maojun Zhang


An active-set projected trust region algorithm is proposed for box constrained optimization problems, where the given algorithm is designed by three steps. First, the projected gradient direction which normally has better numerical performance is introduced. Second, the projected trust region direction that often possesses good convergence is defined, where the matrix of trust region subproblem is updated by limited memory strategy. Third, in order to get both good numerical performance and convergence, the authors define the final search which is the convex combination of the projected gradient direction and the projected trust region direction. Under suitable conditions, the global convergence of the given algorithm is established. Numerical results show that the presented method is competitive to other similar methods.


Active-set strategy convergence trust region 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceGuangxi UniversityNanningChina
  2. 2.School of Mathematic and Computing ScienceGuilin University of Electronic TechnologyGuilinChina

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