Journal of Systems Science and Complexity

, Volume 27, Issue 3, pp 565–580 | Cite as

A nonmonotone filter line search technique for the MBFGS method in unconstrained optimization

  • Zhujun WangEmail author
  • Detong Zhu


This paper presents a new nonmonotone filter line search technique in association with the MBFGS method for solving unconstrained minimization. The filter method, which is traditionally used for constrained nonlinear programming (NLP), is extended to solve unconstrained NLP by converting the latter to an equality constrained minimization. The nonmonotone idea is employed to the filter method so that the restoration phrase, a common feature of most filter methods, is not needed. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. The results of numerical experiments indicate that the proposed method is efficient.

Key words

Convergence filter method MBFGS method nonmonotone technique unconstrained optimization 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.College of ScienceHunan Institute of EngineeringXiangtanChina
  2. 2.Department of MathematicsShanghai Normal UniversityShanghaiChina

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