IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n845017.html

The Space Decomposition Theory for a Class of Semi‐Infinite Maximum Eigenvalue Optimizations

Author

Listed:
  • Ming Huang
  • Li-Ping Pang
  • Xi-Jun Liang
  • Zun-Quan Xia

Abstract

We study optimization problems involving eigenvalues of symmetric matrices. We present a nonsmooth optimization technique for a class of nonsmooth functions which are semi‐infinite maxima of eigenvalue functions. Our strategy uses generalized gradients and 𝒰𝒱 space decomposition techniques suited for the norm and other nonsmooth performance criteria. For the class of max‐functions, which possesses the so‐called primal‐dual gradient structure, we compute smooth trajectories along which certain second‐order expansions can be obtained. We also give the first‐ and second‐order derivatives of primal‐dual function in the space of decision variables Rm under some assumptions.

Suggested Citation

  • Ming Huang & Li-Ping Pang & Xi-Jun Liang & Zun-Quan Xia, 2014. "The Space Decomposition Theory for a Class of Semi‐Infinite Maximum Eigenvalue Optimizations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:845017
    DOI: 10.1155/2014/845017
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/845017
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/845017?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
    ---><---

    References listed on IDEAS

    as
    1. Yuan Lu & Li-Ping Pang & Jie Shen & Xi-Jun Liang, 2012. "A Decomposition Algorithm for Convex Nondifferentiable Minimization with Errors," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, December.
    2. Yuan Lu & Li-Ping Pang & Jie Shen & Xi-Jun Liang, 2012. "A Decomposition Algorithm for Convex Nondifferentiable Minimization with Errors," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    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. Yuan Lu & Wei Wang & Li-Ping Pang & Dan Li, 2013. "A Decomposition Method with Redistributed Subroutine for Constrained Nonconvex Optimization," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnlaaa:v:2014:y:2014:i:1:n:845017. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.