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Globally Convergent BFGS Method for Nonsmooth Convex Optimization1

Author

Listed:
  • A. I. Rauf

    (Hamdard University Islamabad, Markaz)

  • M. Fukushima

    (Kyoto University)

Abstract

We propose an implementable BFGS method for solving a nonsmooth convex optimization problem by converting the original objective function into a once continuously differentiable function by way of the Moreau–Yosida regularization. The proposed method makes use of approximate function and gradient values of the Moreau-Yosida regularization instead of the corresponding exact values. We prove the global convergence of the proposed method under the assumption of strong convexity of the objective function.

Suggested Citation

  • A. I. Rauf & M. Fukushima, 2000. "Globally Convergent BFGS Method for Nonsmooth Convex Optimization1," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 539-558, March.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:3:d:10.1023_a:1004633524446
    DOI: 10.1023/A:1004633524446
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    References listed on IDEAS

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    1. Correa Romar, 2014. "Mathematical Foci," Mathematical Economics Letters, De Gruyter, vol. 2(1-2), pages 5-11, August.
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    Cited by:

    1. Zhou Sheng & Gonglin Yuan, 2018. "An effective adaptive trust region algorithm for nonsmooth minimization," Computational Optimization and Applications, Springer, vol. 71(1), pages 251-271, September.

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