Numerical Algorithms

, Volume 64, Issue 1, pp 1–20 | Cite as

A nonmonotone trust region method with new inexact line search for unconstrained optimization

  • Jinghui Liu
  • Changfeng Ma
Original Paper


In this paper, a new nonmonotone inexact line search rule is proposed and applied to the trust region method for unconstrained optimization problems. In our line search rule, the current nonmonotone term is a convex combination of the previous nonmonotone term and the current objective function value, instead of the current objective function value . We can obtain a larger stepsize in each line search procedure and possess nonmonotonicity when incorporating the nonmonotone term into the trust region method. Unlike the traditional trust region method, the algorithm avoids resolving the subproblem if a trial step is not accepted. Under suitable conditions, global convergence is established. Numerical results show that the new method is effective for solving unconstrained optimization problems.


Unconstrained optimization Inexact line search Trust region method Global convergence Numerical experiments 


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceFujian Normal UniversityFuzhouPeople’s Republic of China

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