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Damped Techniques for the Limited Memory BFGS Method for Large-Scale Optimization

Author

Listed:
  • Mehiddin Al-Baali

    (Sultan Qaboos University)

  • Lucio Grandinetti

    (University of Calabria)

  • Ornella Pisacane

    (Polytechnic University of Marche)

Abstract

This paper is aimed to extend a certain damped technique, suitable for the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method, to the limited memory BFGS method in the case of the large-scale unconstrained optimization. It is shown that the proposed technique maintains the global convergence property on uniformly convex functions for the limited memory BFGS method. Some numerical results are described to illustrate the important role of the damped technique. Since this technique enforces safely the positive definiteness property of the BFGS update for any value of the steplength, we also consider only the first Wolfe–Powell condition on the steplength. Then, as for the backtracking framework, only one gradient evaluation is performed on each iteration. It is reported that the proposed damped methods work much better than the limited memory BFGS method in several cases.

Suggested Citation

  • Mehiddin Al-Baali & Lucio Grandinetti & Ornella Pisacane, 2014. "Damped Techniques for the Limited Memory BFGS Method for Large-Scale Optimization," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 688-699, May.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:2:d:10.1007_s10957-013-0448-8
    DOI: 10.1007/s10957-013-0448-8
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    References listed on IDEAS

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    1. Vincent Malmedy & Philippe Toint, 2011. "Approximating Hessians in unconstrained optimization arising from discretized problems," Computational Optimization and Applications, Springer, vol. 50(1), pages 1-22, September.
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    Cited by:

    1. S. Bojari & M. R. Eslahchi, 2020. "Global convergence of a family of modified BFGS methods under a modified weak-Wolfe–Powell line search for nonconvex functions," 4OR, Springer, vol. 18(2), pages 219-244, June.
    2. Fahimeh Biglari & Farideh Mahmoodpur, 2016. "Scaling Damped Limited-Memory Updates for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 177-188, July.
    3. Mehiddin Al-Baali & Andrea Caliciotti & Giovanni Fasano & Massimo Roma, 2017. "Exploiting damped techniques for nonlinear conjugate gradient methods," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(3), pages 501-522, December.
    4. D. Tarzanagh & M. Peyghami, 2015. "A new regularized limited memory BFGS-type method based on modified secant conditions for unconstrained optimization problems," Journal of Global Optimization, Springer, vol. 63(4), pages 709-728, December.

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