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A regularized limited memory BFGS method for large-scale unconstrained optimization and its efficient implementations

Author

Listed:
  • Hardik Tankaria

    (Kyoto University)

  • Shinji Sugimoto

    (Shimadzu Corpotation)

  • Nobuo Yamashita

    (Kyoto University)

Abstract

The limited memory BFGS (L-BFGS) method is one of the popular methods for solving large-scale unconstrained optimization. Since the standard L-BFGS method uses a line search to guarantee its global convergence, it sometimes requires a large number of function evaluations. To overcome the difficulty, we propose a new L-BFGS with a certain regularization technique. We show its global convergence under the usual assumptions. In order to make the method more robust and efficient, we also extend it with several techniques such as the nonmonotone technique and simultaneous use of the Wolfe line search. Finally, we present some numerical results for test problems in CUTEst, which show that the proposed method is robust in terms of solving more problems.

Suggested Citation

  • Hardik Tankaria & Shinji Sugimoto & Nobuo Yamashita, 2022. "A regularized limited memory BFGS method for large-scale unconstrained optimization and its efficient implementations," Computational Optimization and Applications, Springer, vol. 82(1), pages 61-88, May.
    • Handle: RePEc:spr:coopap:v:82:y:2022:i:1:d:10.1007_s10589-022-00351-5
    DOI: 10.1007/s10589-022-00351-5
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