IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v76y2020i4d10.1007_s10898-020-00875-2.html
   My bibliography  Save this article

A derivative-free algorithm for spherically constrained optimization

Author

Listed:
  • Min Xi

    (Nanjing Normal University
    Guangdong University of Foreign Studies)

  • Wenyu Sun

    (Nanjing Normal University)

  • Yannan Chen

    (South China Normal University)

  • Hailin Sun

    (Nanjing Normal University)

Abstract

Spherically constrained optimization, which minimizes an objective function on a unit sphere, has wide applications in numerical multilinear algebra, signal processing, solid mechanics, etc. In this paper, we consider a certain case that the derivatives of the objective function are unavailable. This case arises frequently in computational science, chemistry, physics, and other enormous areas. To explore the spherical structure of the above problem, we apply the Cayley transform to preserve iterates on the sphere and propose a derivative-free algorithm, which employs a simple model-based trust-region framework. Under mild conditions, global convergence of the proposed algorithm is established. Preliminary numerical experiments illustrate the promising performances of our algorithm.

Suggested Citation

  • Min Xi & Wenyu Sun & Yannan Chen & Hailin Sun, 2020. "A derivative-free algorithm for spherically constrained optimization," Journal of Global Optimization, Springer, vol. 76(4), pages 841-861, April.
  • Handle: RePEc:spr:jglopt:v:76:y:2020:i:4:d:10.1007_s10898-020-00875-2
    DOI: 10.1007/s10898-020-00875-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-020-00875-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10898-020-00875-2?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. C.J. Price & I.D. Coope & D. Byatt, 2002. "A Convergent Variant of the Nelder–Mead Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 5-19, April.
    2. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, June.
    3. Genetha Anne Gray & Tamara G. Kolda & Ken Sale & Malin M. Young, 2004. "Optimizing an Empirical Scoring Function for Transmembrane Protein Structure Determination," INFORMS Journal on Computing, INFORMS, vol. 16(4), pages 406-418, November.
    4. Kazuo Yamaguchi, 2016. "Borda winner in facility location problems on sphere," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 893-898, April.
    Full references (including those not matched with items on IDEAS)

    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. Ian Coope & Rachael Tappenden, 2019. "Efficient calculation of regular simplex gradients," Computational Optimization and Applications, Springer, vol. 72(3), pages 561-588, April.
    2. Kaiwen Ma & Nikolaos V. Sahinidis & Sreekanth Rajagopalan & Satyajith Amaran & Scott J Bury, 2021. "Decomposition in derivative-free optimization," Journal of Global Optimization, Springer, vol. 81(2), pages 269-292, October.
    3. Yasushi Narushima & Shummin Nakayama & Masashi Takemura & Hiroshi Yabe, 2023. "Memoryless Quasi-Newton Methods Based on the Spectral-Scaling Broyden Family for Riemannian Optimization," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 639-664, May.
    4. Saha, Tanay & Rakshit, Suman & Khare, Swanand R., 2023. "Linearly structured quadratic model updating using partial incomplete eigendata," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    5. Guang Li & Paat Rusmevichientong & Huseyin Topaloglu, 2015. "The d -Level Nested Logit Model: Assortment and Price Optimization Problems," Operations Research, INFORMS, vol. 63(2), pages 325-342, April.
    6. Zheng, Sanpeng & Feng, Renzhong, 2023. "A variable projection method for the general radial basis function neural network," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    7. Jörg Fliege & Andrey Tin & Alain Zemkoho, 2021. "Gauss–Newton-type methods for bilevel optimization," Computational Optimization and Applications, Springer, vol. 78(3), pages 793-824, April.
    8. Hai-Jun Wang & Qin Ni, 2010. "A Convex Approximation Method For Large Scale Linear Inequality Constrained Minimization," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(01), pages 85-101.
    9. Chen, Liang, 2016. "A high-order modified Levenberg–Marquardt method for systems of nonlinear equations with fourth-order convergence," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 79-93.
    10. Ji, Li-Qun, 2015. "An assessment of agricultural residue resources for liquid biofuel production in China," Renewable and Sustainable Energy Reviews, Elsevier, vol. 44(C), pages 561-575.
    11. Babaie-Kafaki, Saman & Ghanbari, Reza, 2014. "The Dai–Liao nonlinear conjugate gradient method with optimal parameter choices," European Journal of Operational Research, Elsevier, vol. 234(3), pages 625-630.
    12. Marko Miladinović & Predrag Stanimirović & Sladjana Miljković, 2011. "Scalar Correction Method for Solving Large Scale Unconstrained Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 304-320, November.
    13. Wei Bian & Xiaojun Chen, 2017. "Optimality and Complexity for Constrained Optimization Problems with Nonconvex Regularization," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1063-1084, November.
    14. Yutao Zheng & Bing Zheng, 2017. "Two New Dai–Liao-Type Conjugate Gradient Methods for Unconstrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 502-509, November.
    15. Xiaojing Zhu & Hiroyuki Sato, 2020. "Riemannian conjugate gradient methods with inverse retraction," Computational Optimization and Applications, Springer, vol. 77(3), pages 779-810, December.
    16. Henri Bonnel & C. Yalçın Kaya, 2010. "Optimization Over the Efficient Set of Multi-objective Convex Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 93-112, October.
    17. Li, Jinqing & Ma, Jun, 2019. "Maximum penalized likelihood estimation of additive hazards models with partly interval censoring," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 170-180.
    18. Zohre Aminifard & Saman Babaie-Kafaki, 2019. "An optimal parameter choice for the Dai–Liao family of conjugate gradient methods by avoiding a direction of the maximum magnification by the search direction matrix," 4OR, Springer, vol. 17(3), pages 317-330, September.
    19. Chen, Wang & Yang, Xinmin & Zhao, Yong, 2023. "Memory gradient method for multiobjective optimization," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    20. Abolfazl Gharaei & Alireza Amjadian & Ali Shavandi & Amir Amjadian, 2023. "An augmented Lagrangian approach with general constraints to solve nonlinear models of the large-scale reliable inventory systems," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-37, March.

    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:spr:jglopt:v:76:y:2020:i:4:d:10.1007_s10898-020-00875-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.