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Eigenvalue Analyses on the Memoryless Davidon–Fletcher–Powell Method Based on a Spectral Secant Equation

Author

Listed:
  • Fatemeh Dargahi

    (Semnan University)

  • Saman Babaie-Kafaki

    (Free University of Bozen-Bolzano)

  • Zohre Aminifard

    (Semnan University)

Abstract

The subject of this study is the analysis of the spectral secant equation for the well-known Davidon–Fletcher–Powell (DFP) quasi-Newton updating formula. More precisely, we plan to make the memoryless DFP formula well conditioned in several aspects. We first focus our efforts on obtaining eigenvalues of the DFP formula and directly analyzing its spectral condition number. Then, we proceed in a different direction by using the Byrd–Nocedal measure function as well. Lastly, we propose a hybrid adaptive formula for the spectral parameter of the method.

Suggested Citation

  • Fatemeh Dargahi & Saman Babaie-Kafaki & Zohre Aminifard, 2024. "Eigenvalue Analyses on the Memoryless Davidon–Fletcher–Powell Method Based on a Spectral Secant Equation," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 394-403, January.
    • Handle: RePEc:spr:joptap:v:200:y:2024:i:1:d:10.1007_s10957-023-02354-6
    DOI: 10.1007/s10957-023-02354-6
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    References listed on IDEAS

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    1. Saman Babaie-Kafaki, 2015. "On Optimality of the Parameters of Self-Scaling Memoryless Quasi-Newton Updating Formulae," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 91-101, October.
    2. D. Pu, 2002. "Convergence of the DFP Algorithm Without Exact Line Search," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 187-211, January.
    3. Chengxian Xu & Jianzhong Zhang, 2001. "A Survey of Quasi-Newton Equations and Quasi-Newton Methods for Optimization," Annals of Operations Research, Springer, vol. 103(1), pages 213-234, March.
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