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A New Modified Barzilai–Borwein Gradient Method for the Quadratic Minimization Problem

Author

Listed:
  • Yutao Zheng

    (Lanzhou University)

  • Bing Zheng

    (Lanzhou University)

Abstract

A new modified Barzilai–Borwein gradient method for solving the strictly convex quadratic minimization problem is proposed by properly changing the Barzilai–Borwein stepsize such that some certain multi-step quasi-Newton condition is satisfied. The global convergence is analyzed. Numerical experiments show that the new method can outperform some known gradient methods.

Suggested Citation

  • Yutao Zheng & Bing Zheng, 2017. "A New Modified Barzilai–Borwein Gradient Method for the Quadratic Minimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 179-186, January.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:1:d:10.1007_s10957-016-1008-9
    DOI: 10.1007/s10957-016-1008-9
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    References listed on IDEAS

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    1. Clóvis Gonzaga & Ruana Schneider, 2016. "On the steepest descent algorithm for quadratic functions," Computational Optimization and Applications, Springer, vol. 63(2), pages 523-542, March.
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    Cited by:

    1. Behzad Azmi & Karl Kunisch, 2020. "Analysis of the Barzilai-Borwein Step-Sizes for Problems in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 819-844, June.

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