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Dynamic scaling on the limited memory BFGS method

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  • Biglari, Fahimeh

Abstract

This paper describes a limited-memory quasi-Newton method in which the initial inverse Hessian approximation is constructed based on the concept of equilibration of the inverse Hessian matrix. Curvature information about the objective function is stored in the form of a diagonal matrix, and plays the dual role of providing an initial matrix and of equilibrating for limited memory BFGS (LBFGS) iterations. An extensive numerical testing has been performed showing that the diagonal scaling strategy proposed is very effective.

Suggested Citation

  • Biglari, Fahimeh, 2015. "Dynamic scaling on the limited memory BFGS method," European Journal of Operational Research, Elsevier, vol. 243(3), pages 697-702.
    • Handle: RePEc:eee:ejores:v:243:y:2015:i:3:p:697-702
    DOI: 10.1016/j.ejor.2014.12.050
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    References listed on IDEAS

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    1. Michael H. Schneider & Stavros A. Zenios, 1990. "A Comparative Study of Algorithms for Matrix Balancing," Operations Research, INFORMS, vol. 38(3), pages 439-455, June.
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    Cited by:

    1. 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.
    2. Xue, Zhenqian & Zhang, Kai & Zhang, Chi & Ma, Haoming & Chen, Zhangxin, 2023. "Comparative data-driven enhanced geothermal systems forecasting models: A case study of Qiabuqia field in China," Energy, Elsevier, vol. 280(C).

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