IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v65y2016i4d10.1007_s10898-016-0402-z.html
   My bibliography  Save this article

Projection algorithms for nonconvex minimization with application to sparse principal component analysis

Author

Listed:
  • William W. Hager

    (University of Florida)

  • Dzung T. Phan

    (IBM T. J. Watson Research Center)

  • Jiajie Zhu

    (University of Florida
    Boston College)

Abstract

We consider concave minimization problems over nonconvex sets. Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient projection algorithm and an approximate Newton algorithm where the Hessian approximation is a multiple of the identity. Convergence results are established. In numerical experiments arising in sparse principal component analysis, it is seen that the performance of the gradient projection algorithm is very similar to that of the truncated power method and the generalized power method. In some cases, the approximate Newton algorithm with a Barzilai–Borwein Hessian approximation and a nonmonotone line search can be substantially faster than the other algorithms, and can converge to a better solution.

Suggested Citation

  • William W. Hager & Dzung T. Phan & Jiajie Zhu, 2016. "Projection algorithms for nonconvex minimization with application to sparse principal component analysis," Journal of Global Optimization, Springer, vol. 65(4), pages 657-676, August.
    • Handle: RePEc:spr:jglopt:v:65:y:2016:i:4:d:10.1007_s10898-016-0402-z
    DOI: 10.1007/s10898-016-0402-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-016-0402-z
    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/s10898-016-0402-z?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. Akiko Takeda & Mahesan Niranjan & Jun-ya Gotoh & Yoshinobu Kawahara, 2013. "Simultaneous pursuit of out-of-sample performance and sparsity in index tracking portfolios," Computational Management Science, Springer, vol. 10(1), pages 21-49, February.
    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. Dzung T. Phan & Matt Menickelly, 2021. "On the Solution of ℓ 0 -Constrained Sparse Inverse Covariance Estimation Problems," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 531-550, May.

    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. Yu Zheng & Bowei Chen & Timothy M. Hospedales & Yongxin Yang, 2019. "Index Tracking with Cardinality Constraints: A Stochastic Neural Networks Approach," Papers 1911.05052, arXiv.org, revised Nov 2019.
    2. Yu Zheng & Timothy M. Hospedales & Yongxin Yang, 2018. "Diversity and Sparsity: A New Perspective on Index Tracking," Papers 1809.01989, arXiv.org, revised Feb 2020.
    3. Hongxin Zhao & Lingchen Kong & Hou-Duo Qi, 2021. "Optimal portfolio selections via $$\ell _{1, 2}$$ ℓ 1 , 2 -norm regularization," Computational Optimization and Applications, Springer, vol. 80(3), pages 853-881, December.
    4. Strub, O. & Baumann, P., 2018. "Optimal construction and rebalancing of index-tracking portfolios," European Journal of Operational Research, Elsevier, vol. 264(1), pages 370-387.
    5. Gnägi, M. & Strub, O., 2020. "Tracking and outperforming large stock-market indices," Omega, Elsevier, vol. 90(C).
    6. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2022. "Sparsity and stability for minimum-variance portfolios," Risk Management, Palgrave Macmillan, vol. 24(3), pages 214-235, September.
    7. Yen, Yu-Min & Yen, Tso-Jung, 2014. "Solving norm constrained portfolio optimization via coordinate-wise descent algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 737-759.
    8. Eisuke Yamagata & Shunsuke Ono, 2023. "Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via $\ell_0$-Constrained Portfolio," Papers 2309.10152, arXiv.org, revised Mar 2024.
    9. Chungen Shen & Xiao Liu, 2021. "Solving nonnegative sparsity-constrained optimization via DC quadratic-piecewise-linear approximations," Journal of Global Optimization, Springer, vol. 81(4), pages 1019-1055, December.
    10. Zhiping Chen & Xinkai Zhuang & Jia Liu, 2019. "A Sustainability-Oriented Enhanced Indexation Model with Regime Switching and Cardinality Constraint," Sustainability, MDPI, vol. 11(15), pages 1-14, July.
    11. Margherita Giuzio & Kay Eichhorn-Schott & Sandra Paterlini & Vincent Weber, 2018. "Tracking hedge funds returns using sparse clones," Annals of Operations Research, Springer, vol. 266(1), pages 349-371, July.
    12. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2019. "Sparsity and Stability for Minimum-Variance Portfolios," Papers 1910.11840, arXiv.org.

    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:65:y:2016:i:4:d:10.1007_s10898-016-0402-z. 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.