Skip to main content
Springer Nature Link
Log in

An improved adaptive trust-region algorithm

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

This paper gives a variant trust-region method, where its radius is automatically adjusted by using the model information gathered at the current and preceding iterations. The primary aim is to decrease the number of function evaluations and solving subproblems, which increases the efficiency of the trust-region method. The next aim is to update the new radius for large-scale problems without imposing too much computational cost to the scheme. Global convergence to first-order stationary points is proved under classical assumptions. Preliminary numerical experiments on a set of test problems from the CUTEst collection show that the presented method is promising for solving unconstrained optimization problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Ahookhosh, M., Amini, K.: A nonmonotone trust region method with adaptive radius for unconstrained optimization. Comput. Math. Appl. 60, 411–422 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ahookhosh, M., Esmaeili, H., Kimiaei, M.: An effective trust-region-based approach for symmetric nonlinear systems. Int. J. Comput. Math. 90(3), 671–690 (2013)

    Article  MATH  Google Scholar 

  3. Amini, K., Ahookhosh, M.: A hybrid of adjustable trust-region and nonmonotone algorithms for unconstrained optimization. Appl. Math. Modell. 38, 2601–2612 (2014)

    Article  MathSciNet  Google Scholar 

  4. Conn, A.R., Gould, N.I.M., Toint, PhL: Trust Region Methods. Society for Industrial and Applied Mathematics. SIAM, Philadelphia (2000)

    Book  Google Scholar 

  5. Dolan, E., Moré, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201–213 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gould, N.I.M., Orban, D., Toint, Ph.L.: CUTEst: a constrained and unconstrained testing environment with safe threads for mathematical optimization. Comput. Optim. Appl. 60, 545–557 (2015)

  7. Gould, N.I.M., Orban, D., Sartenaer, A., Toint, PhL: Sensitivity of trust region algorithms to their parameters. Q. J. Oper. Res. 3, 227–241 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Li, D.H., Fukushima, M.: A modified BFGS method and its global convergence in nonconvex minimization. J. Comput. Appl. Math. 129, 15–35 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, NewYork (2006)

    MATH  Google Scholar 

  10. Sartenaer, A.: Automatic determination of an initial trust region in nonlinear programming. SIAM J. Sci. Comput. 18(6), 1788–1803 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  11. Schnabel, R.B., Eskow, E.: A new modified Cholesky factorization. SIAM J. Sci. Comput. 11(6), 1136–1158 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  12. Shi, Z.J., Guo, J.H.: A new trust region method with adaptive radius. Comput. Optim. Appl. 41, 225–242 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Walmag, J.M.B., Delhez, E.J.M.: A note on trust region radius update. SIAM J. Optim. 16(2), 548–562 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. Xiao, Y., Sun, H., Wang, Z.: A globally convergent BFGS method with nonmonotone line search for non-convex minimization. J. Comput. Appl. Math. 230, 95–106 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zhang, X.S., Zhang, J.L., Liao, L.Z.: An adaptive trust region method and its convergence. Sci. China 45, 620–631 (2002)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

We are very thankful to two anonymous referees for careful reading and many useful suggestions, which improve the paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah, Iran

    Ahmad Kamandi & Keyvan Amini

  2. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Masoud Ahookhosh

Authors
  1. Ahmad Kamandi
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Keyvan Amini
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Masoud Ahookhosh
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Keyvan Amini.

Appendix

Appendix

See Table 3 for the list of test problems from the CUTEst collection.

Table 3 List of test problems
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kamandi, A., Amini, K. & Ahookhosh, M. An improved adaptive trust-region algorithm. Optim Lett 11, 555–569 (2017). https://doi.org/10.1007/s11590-016-1018-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-016-1018-4

Keywords