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New Inexact Line Search Method for Unconstrained Optimization

Author

Listed:
  • Z. J. Shi

    (Qufu Normal University
    Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

  • J. Shen

    (University of Michigan)

Abstract

We propose a new inexact line search rule and analyze the global convergence and convergence rate of related descent methods. The new line search rule is similar to the Armijo line-search rule and contains it as a special case. We can choose a larger stepsize in each line-search procedure and maintain the global convergence of related line-search methods. This idea can make us design new line-search methods in some wider sense. In some special cases, the new descent method can reduce to the Barzilai and Borewein method. Numerical results show that the new line-search methods are efficient for solving unconstrained optimization problems.

Suggested Citation

  • Z. J. Shi & J. Shen, 2005. "New Inexact Line Search Method for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 127(2), pages 425-446, November.
    • Handle: RePEc:spr:joptap:v:127:y:2005:i:2:d:10.1007_s10957-005-6553-6
    DOI: 10.1007/s10957-005-6553-6
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    Citations

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    Cited by:

    1. Vieira, Douglas Alexandre Gomes & Lisboa, Adriano Chaves, 2014. "Line search methods with guaranteed asymptotical convergence to an improving local optimum of multimodal functions," European Journal of Operational Research, Elsevier, vol. 235(1), pages 38-46.
    2. Antoine Soubeyran, 2022. "Variational rationality. Self regulation success as a succession of worthwhile moves that make sufficient progress," Working Papers hal-04041238, HAL.
    3. Shi, Zhenjun & Wang, Shengquan, 2011. "Nonmonotone adaptive trust region method," European Journal of Operational Research, Elsevier, vol. 208(1), pages 28-36, January.
    4. Antoine Soubeyran, 2023. "Variational rationality. Self regulation success as a succession of worthwhile moves that make sufficient progress," AMSE Working Papers 2307, Aix-Marseille School of Economics, France.
    5. Ping Hu & Xu-Qing Liu, 2013. "A Nonmonotone Line Search Slackness Technique for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 158(3), pages 773-786, September.
    6. Zhiguang Zhang, 2010. "A New Method for Unconstrained Optimization Problem," Modern Applied Science, Canadian Center of Science and Education, vol. 4(10), pages 133-133, October.
    7. Zhang, Qiang & Liu, Jijun, 2024. "On fluorophore imaging by nonlinear diffusion model with dynamical iterative scheme," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 533-549.
    8. Sheng-Tong Zhou & Di Wang & Qian Xiao & Jian-min Zhou & Hong-Guang Li & Wen-Bing Tu, 2021. "An improved first order reliability method based on modified Armijo rule and interpolation-based backtracking scheme," Journal of Risk and Reliability, , vol. 235(2), pages 209-229, April.
    9. Long, Jiancheng & Szeto, W.Y., 2019. "Congestion and environmental toll schemes for the morning commute with heterogeneous users and parallel routes," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 305-333.

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