IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v64y2016i2d10.1007_s10589-015-9812-y.html
   My bibliography  Save this article

On how to solve large-scale log-determinant optimization problems

Author

Listed:
  • Chengjing Wang

    (Southwest Jiaotong University)

Abstract

We propose a proximal augmented Lagrangian method and a hybrid method, i.e., employing the proximal augmented Lagrangian method to generate a good initial point and then employing the Newton-CG augmented Lagrangian method to get a highly accurate solution, to solve large-scale nonlinear semidefinite programming problems whose objective functions are a sum of a convex quadratic function and a log-determinant term. We demonstrate that the algorithms can supply a high quality solution efficiently even for some ill-conditioned problems.

Suggested Citation

  • Chengjing Wang, 2016. "On how to solve large-scale log-determinant optimization problems," Computational Optimization and Applications, Springer, vol. 64(2), pages 489-511, June.
    • Handle: RePEc:spr:coopap:v:64:y:2016:i:2:d:10.1007_s10589-015-9812-y
    DOI: 10.1007/s10589-015-9812-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-015-9812-y
    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/s10589-015-9812-y?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. Defeng Sun, 2006. "The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 761-776, November.
    2. Zhaolin Hu & Jing Cao & L. Jeff Hong, 2012. "Robust Simulation of Global Warming Policies Using the DICE Model," Management Science, INFORMS, vol. 58(12), pages 2190-2206, December.
    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. Takashi Nakagaki & Mituhiro Fukuda & Sunyoung Kim & Makoto Yamashita, 2020. "A dual spectral projected gradient method for log-determinant semidefinite problems," Computational Optimization and Applications, Springer, vol. 76(1), pages 33-68, May.
    2. Chengjing Wang & Peipei Tang, 2017. "A primal majorized semismooth Newton-CG augmented Lagrangian method for large-scale linearly constrained convex programming," Computational Optimization and Applications, Springer, vol. 68(3), pages 503-532, December.

    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. Jie Wu & Zhixin Chen & Xiang Ji, 2020. "Sustainable trade promotion decisions under demand disruption in manufacturer-retailer supply chains," Annals of Operations Research, Springer, vol. 290(1), pages 115-143, July.
    2. Liwei Zhang & Shengzhe Gao & Saoyan Guo, 2019. "Statistical Inference of Second-Order Cone Programming," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(02), pages 1-17, April.
    3. Weiwei Fan & L. Jeff Hong & Xiaowei Zhang, 2020. "Distributionally Robust Selection of the Best," Management Science, INFORMS, vol. 66(1), pages 190-208, January.
    4. Qi Zhao & Zhongwen Chen, 2018. "An SQP-type Method with Superlinear Convergence for Nonlinear Semidefinite Programming," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(03), pages 1-25, June.
    5. Houduo Qi, 2009. "Local Duality of Nonlinear Semidefinite Programming," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 124-141, February.
    6. H. Wu & H. Luo & J. Yang, 2014. "Nonlinear separation approach for the augmented Lagrangian in nonlinear semidefinite programming," Journal of Global Optimization, Springer, vol. 59(4), pages 695-727, August.
    7. Diethard Klatte & Bernd Kummer, 2013. "Aubin property and uniqueness of solutions in cone constrained optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 291-304, June.
    8. Yun Wang & Liwei Zhang, 2009. "Properties of equation reformulation of the Karush–Kuhn–Tucker condition for nonlinear second order cone optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(2), pages 195-218, October.
    9. Jia Wu & Yi Zhang & Liwei Zhang & Yue Lu, 2016. "A Sequential Convex Program Approach to an Inverse Linear Semidefinite Programming Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-26, August.
    10. Wei, Yi-Ming & Mi, Zhi-Fu & Huang, Zhimin, 2015. "Climate policy modeling: An online SCI-E and SSCI based literature review," Omega, Elsevier, vol. 57(PA), pages 70-84.
    11. Boris S. Mordukhovich & T. T. A. Nghia, 2014. "Nonsmooth Cone-Constrained Optimization with Applications to Semi-Infinite Programming," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 301-324, May.
    12. Soumyadip Ghosh & Henry Lam, 2019. "Robust Analysis in Stochastic Simulation: Computation and Performance Guarantees," Operations Research, INFORMS, vol. 67(1), pages 232-249, January.
    13. H. Luo & H. Wu & G. Chen, 2012. "On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming," Journal of Global Optimization, Springer, vol. 54(3), pages 599-618, November.
    14. Fangzhi Wang & Hua Liao & Richard S. J. Tol & Changjing Ji, 2024. "Endogenous Preference for Nonmarket Goods in Carbon Abatement Decisions," Decision Analysis, INFORMS, vol. 21(4), pages 235-251, December.
    15. B. S. Mordukhovich & T. T. A. Nghia & R. T. Rockafellar, 2015. "Full Stability in Finite-Dimensional Optimization," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 226-252, February.
    16. Yanikoglu, I. & den Hertog, D. & Kleijnen, Jack P.C., 2013. "Adjustable Robust Parameter Design with Unknown Distributions," Discussion Paper 2013-022, Tilburg University, Center for Economic Research.
    17. Jérôme Bolte & Aris Daniilidis & Adrian S. Lewis, 2011. "Generic Optimality Conditions for Semialgebraic Convex Programs," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 55-70, February.
    18. Aleksandrina Goeva & Henry Lam & Huajie Qian & Bo Zhang, 2019. "Optimization-Based Calibration of Simulation Input Models," Operations Research, INFORMS, vol. 67(5), pages 1362-1382, September.
    19. Jianzhong Zhang & Liwei Zhang & Xiantao Xiao, 2010. "A Perturbation approach for an inverse quadratic programming problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(3), pages 379-404, December.
    20. Liwei Zhang & Shaoyan Guo & Jia Wu & Shoulin Hao, 2013. "Nonsingularity in matrix conic optimization induced by spectral norm via a smoothing metric projector," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(3), pages 373-404, December.

    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:64:y:2016:i:2:d:10.1007_s10589-015-9812-y. 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.