IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v235y2014i1p38-46.html
   My bibliography  Save this article

Line search methods with guaranteed asymptotical convergence to an improving local optimum of multimodal functions

Author

Listed:
  • Vieira, Douglas Alexandre Gomes
  • Lisboa, Adriano Chaves

Abstract

This paper considers line search optimization methods using a mathematical framework based on the simple concept of a v-pattern and its properties. This framework provides theoretical guarantees on preserving, in the localizing interval, a local optimum no worse than the starting point. Notably, the framework can be applied to arbitrary unidimensional functions, including multimodal and infinitely valued ones. Enhanced versions of the golden section, bisection and Brent’s methods are proposed and analyzed within this framework: they inherit the improving local optimality guarantee. Under mild assumptions the enhanced algorithms are proved to converge to a point in the solution set in a finite number of steps or that all their accumulation points belong to the solution set.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:235:y:2014:i:1:p:38-46
    DOI: 10.1016/j.ejor.2013.12.041
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713010254
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.12.041?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ivorra, Benjamin & Mohammadi, Bijan & Manuel Ramos, Angel, 2015. "A multi-layer line search method to improve the initialization of optimization algorithms," European Journal of Operational Research, Elsevier, vol. 247(3), pages 711-720.
    2. Mina Torabi & Mohammad-Mehdi Hosseini, 2018. "A New Descent Algorithm Using the Three-Step Discretization Method for Solving Unconstrained Optimization Problems," Mathematics, MDPI, vol. 6(4), pages 1-18, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    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. 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.
    5. 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.
    6. Antoine Soubeyran, 2022. "Variational rationality. Self regulation success as a succession of worthwhile moves that make sufficient progress," Working Papers hal-04041238, HAL.
    7. 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.
    8. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:235:y:2014:i:1:p:38-46. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.