IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v71y2018i2d10.1007_s10589-018-0010-6.html
   My bibliography  Save this article

A penalty method for rank minimization problems in symmetric matrices

Author

Listed:
  • Xin Shen

    (Rensselaer Polytechnic Institute)

  • John E. Mitchell

    (Rensselaer Polytechnic Institute)

Abstract

The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be cast equivalently as a semidefinite program with complementarity constraints (SDCMPCC). The formulation requires two positive semidefinite matrices to be complementary. This is a continuous and nonconvex reformulation of the rank minimization problem. We investigate calmness of locally optimal solutions to the SDCMPCC formulation and hence show that any locally optimal solution is a KKT point. We develop a penalty formulation of the problem. We present calmness results for locally optimal solutions to the penalty formulation. We also develop a proximal alternating linearized minimization (PALM) scheme for the penalty formulation, and investigate the incorporation of a momentum term into the algorithm. Computational results are presented.

Suggested Citation

  • Xin Shen & John E. Mitchell, 2018. "A penalty method for rank minimization problems in symmetric matrices," Computational Optimization and Applications, Springer, vol. 71(2), pages 353-380, November.
    • Handle: RePEc:spr:coopap:v:71:y:2018:i:2:d:10.1007_s10589-018-0010-6
    DOI: 10.1007/s10589-018-0010-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-018-0010-6
    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/s10589-018-0010-6?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. J. Zhai & X. X. Huang, 2014. "Calmness and Exact Penalization in Vector Optimization under Nonlinear Perturbations," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 856-872, September.
    2. Nathan Krislock & Henry Wolkowicz, 2012. "Euclidean Distance Matrices and Applications," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 879-914, Springer.
    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. April Sagan & John E. Mitchell, 2021. "Low-rank factorization for rank minimization with nonconvex regularizers," Computational Optimization and Applications, Springer, vol. 79(2), pages 273-300, June.
    2. April Sagan & Xin Shen & John E. Mitchell, 2020. "Two Relaxation Methods for Rank Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 806-825, September.

    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. Marcin Bukowski & Janusz Majewski & Agnieszka Sobolewska, 2023. "The Environmental Impact of Changes in the Structure of Electricity Sources in Europe," Energies, MDPI, vol. 16(1), pages 1-22, January.
    2. Nathanaël Randriamihamison & Nathalie Vialaneix & Pierre Neuvial, 2021. "Applicability and Interpretability of Ward’s Hierarchical Agglomerative Clustering With or Without Contiguity Constraints," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 363-389, July.
    3. Varvitsiotis, A., 2013. "Combinatorial conditions for low rank solutions in semidefinite programming," Other publications TiSEM d0fcc572-daaf-4bd9-95db-1, Tilburg University, School of Economics and Management.

    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:coopap:v:71:y:2018:i:2:d:10.1007_s10589-018-0010-6. 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.