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Self-Scaling Variable Metric (SSVM) Algorithms

Author

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  • Shmuel S. Oren

    (Xerox Corporation, Palo Alto, California and Stanford University)

Abstract

This part of the paper introduces some possible implementations of Self-Scaling Variable Metric algorithms based on the theory presented in Part I. These implementations are analyzed theoretically and discussed qualitatively. A special class of SSVM algorithms is introduced, which has the additional property of being invariant under scaling of the objective function or of the variables. Experimental results are provided for a particular case of this class. This case has been tested in comparison to the DFP algorithm on a variety of functions with up to 50 variables. The results indicate that the new method has substantial advantage for functions with a large number of variables.

Suggested Citation

  • Shmuel S. Oren, 1974. "Self-Scaling Variable Metric (SSVM) Algorithms," Management Science, INFORMS, vol. 20(5), pages 863-874, January.
    • Handle: RePEc:inm:ormnsc:v:20:y:1974:i:5:p:863-874
    DOI: 10.1287/mnsc.20.5.863
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    Cited by:

    1. S. Cipolla & C. Di Fiore & P. Zellini, 2020. "A variation of Broyden class methods using Householder adaptive transforms," Computational Optimization and Applications, Springer, vol. 77(2), pages 433-463, November.
    2. C. X. Kou & Y. H. Dai, 2015. "A Modified Self-Scaling Memoryless Broyden–Fletcher–Goldfarb–Shanno Method for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 209-224, April.
    3. M. Al-Baali, 1998. "Numerical Experience with a Class of Self-Scaling Quasi-Newton Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 96(3), pages 533-553, March.
    4. Saman Babaie-Kafaki & Reza Ghanbari, 2017. "A class of adaptive Dai–Liao conjugate gradient methods based on the scaled memoryless BFGS update," 4OR, Springer, vol. 15(1), pages 85-92, March.
    5. Martin Buhmann & Dirk Siegel, 2021. "Implementing and modifying Broyden class updates for large scale optimization," Computational Optimization and Applications, Springer, vol. 78(1), pages 181-203, January.
    6. 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.
    7. 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.
    8. Nataj, Sarah & Lui, S.H., 2020. "Superlinear convergence of nonlinear conjugate gradient method and scaled memoryless BFGS method based on assumptions about the initial point," Applied Mathematics and Computation, Elsevier, vol. 369(C).

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