IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v53y2012i1p45-89.html
   My bibliography  Save this article

An inexact spectral bundle method for convex quadratic semidefinite programming

Author

Listed:
  • Huiling Lin

Abstract

We present an inexact spectral bundle method for solving convex quadratic semidefinite optimization problems. This method is a first-order method, hence requires much less computational cost in each iteration than second-order approaches such as interior-point methods. In each iteration of our method, we solve an eigenvalue minimization problem inexactly, and solve a small convex quadratic semidefinite program as a subproblem. We give a proof of the global convergence of this method using techniques from the analysis of the standard bundle method, and provide a global error bound under a Slater type condition for the problem in question. Numerical experiments with matrices of order up to 3000 are performed, and the computational results establish the effectiveness of this method. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Huiling Lin, 2012. "An inexact spectral bundle method for convex quadratic semidefinite programming," Computational Optimization and Applications, Springer, vol. 53(1), pages 45-89, September.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:1:p:45-89
    DOI: 10.1007/s10589-011-9443-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-011-9443-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-011-9443-x?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. Sun, Jie & Zhang, Su, 2010. "A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1210-1220, December.
    2. Jia-Wang Nie & Ya-Xiang Yuan, 2001. "A Predictor–Corrector Algorithm for QSDP Combining Dikin-Type and Newton Centering Steps," Annals of Operations Research, Springer, vol. 103(1), pages 115-133, March.
    3. Grégory Emiel & Claudia Sagastizábal, 2010. "Incremental-like bundle methods with application to energy planning," Computational Optimization and Applications, Springer, vol. 46(2), pages 305-332, June.
    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. Lv, Jian & Pang, Li-Ping & Wang, Jin-He, 2015. "Special backtracking proximal bundle method for nonconvex maximum eigenvalue optimization," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 635-651.

    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. Baha Alzalg & Asma Gafour, 2023. "Convergence of a Weighted Barrier Algorithm for Stochastic Convex Quadratic Semidefinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 490-515, February.
    2. Fan-Yun Meng & Li-Ping Pang & Jian Lv & Jin-He Wang, 2017. "An approximate bundle method for solving nonsmooth equilibrium problems," Journal of Global Optimization, Springer, vol. 68(3), pages 537-562, July.
    3. Sofia Zaourar & Jérôme Malick, 2013. "Prices stabilization for inexact unit-commitment problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(3), pages 341-359, December.
    4. Xiaoliang Wang & Liping Pang & Qi Wu & Mingkun Zhang, 2021. "An Adaptive Proximal Bundle Method with Inexact Oracles for a Class of Nonconvex and Nonsmooth Composite Optimization," Mathematics, MDPI, vol. 9(8), pages 1-27, April.
    5. Xiaodi Bai & Jie Sun & Xiaojin Zheng, 2021. "An Augmented Lagrangian Decomposition Method for Chance-Constrained Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 1056-1069, July.
    6. Bingsheng He & Min Tao & Xiaoming Yuan, 2017. "Convergence Rate Analysis for the Alternating Direction Method of Multipliers with a Substitution Procedure for Separable Convex Programming," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 662-691, August.
    7. Houduo Qi, 2009. "Local Duality of Nonlinear Semidefinite Programming," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 124-141, February.
    8. W. Hare & C. Sagastizábal & M. Solodov, 2016. "A proximal bundle method for nonsmooth nonconvex functions with inexact information," Computational Optimization and Applications, Springer, vol. 63(1), pages 1-28, January.
    9. Guoyong Gu & Bingsheng He & Xiaoming Yuan, 2014. "Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: a unified approach," Computational Optimization and Applications, Springer, vol. 59(1), pages 135-161, October.
    10. Li-Ping Pang & Jian Lv & Jin-He Wang, 2016. "Constrained incremental bundle method with partial inexact oracle for nonsmooth convex semi-infinite programming problems," Computational Optimization and Applications, Springer, vol. 64(2), pages 433-465, June.
    11. Sun, Jie & Zhang, Su, 2010. "A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1210-1220, December.
    12. Liping Pang & Xiaoliang Wang & Fanyun Meng, 2023. "A proximal bundle method for a class of nonconvex nonsmooth composite optimization problems," Journal of Global Optimization, Springer, vol. 86(3), pages 589-620, July.
    13. Xingcai Zhou & Yu Xiang, 2022. "ADMM-Based Differential Privacy Learning for Penalized Quantile Regression on Distributed Functional Data," Mathematics, MDPI, vol. 10(16), pages 1-28, August.
    14. Jian Lv & Li-Ping Pang & Fan-Yun Meng, 2018. "A proximal bundle method for constrained nonsmooth nonconvex optimization with inexact information," Journal of Global Optimization, Springer, vol. 70(3), pages 517-549, March.
    15. N. Hoseini Monjezi & S. Nobakhtian, 2022. "An inexact multiple proximal bundle algorithm for nonsmooth nonconvex multiobjective optimization problems," Annals of Operations Research, Springer, vol. 311(2), pages 1123-1154, April.
    16. Min Tao, 2020. "Convergence study of indefinite proximal ADMM with a relaxation factor," Computational Optimization and Applications, Springer, vol. 77(1), pages 91-123, September.
    17. Min Tao & Xiaoming Yuan, 2018. "On Glowinski’s Open Question on the Alternating Direction Method of Multipliers," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 163-196, October.
    18. M. H. Xu & T. Wu, 2011. "A Class of Linearized Proximal Alternating Direction Methods," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 321-337, November.
    19. Deren Han & Xiaoming Yuan & Wenxing Zhang & Xingju Cai, 2013. "An ADM-based splitting method for separable convex programming," Computational Optimization and Applications, Springer, vol. 54(2), pages 343-369, March.
    20. Deren Han & Xiaoming Yuan, 2012. "A Note on the Alternating Direction Method of Multipliers," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 227-238, October.

    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:53:y:2012:i:1:p:45-89. 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.