IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v56y2013i1p81-96.html
   My bibliography  Save this article

A homotopy method for nonlinear semidefinite programming

Author

Listed:
  • Li Yang
  • Bo Yu

Abstract

In this paper, for solving the nonlinear semidefinite programming problem, a homotopy is constructed by using the parameterized matrix inequality constraint. Existence of a smooth path determined by the homotopy equation, which starts from almost everywhere and converges to a Karush–Kuhn–Tucker point, is proven under mild conditions. A predictor-corrector algorithm is given for numerically tracing the smooth path. Numerical tests with nonlinear semidefinite programming formulations of several control design problems with the data contained in COMPl e ib are done. Numerical results show that the proposed algorithm is feasible and applicable. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Li Yang & Bo Yu, 2013. "A homotopy method for nonlinear semidefinite programming," Computational Optimization and Applications, Springer, vol. 56(1), pages 81-96, September.
    • Handle: RePEc:spr:coopap:v:56:y:2013:i:1:p:81-96
    DOI: 10.1007/s10589-013-9545-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-013-9545-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-013-9545-8?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. NESTEROV , Yurii & TODD , Michael, 1995. "Primal-Dual Interior-Point Methods for Self-Scaled Cones," LIDAM Discussion Papers CORE 1995044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Yuya Yamakawa & Takayuki Okuno, 2022. "A stabilized sequential quadratic semidefinite programming method for degenerate nonlinear semidefinite programs," Computational Optimization and Applications, Springer, vol. 83(3), pages 1027-1064, December.
    2. Li Yang & Bo Yu & YanXi Li, 2015. "A homotopy method based on penalty function for nonlinear semidefinite programming," Journal of Global Optimization, Springer, vol. 63(1), pages 61-76, 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. Luo, Z-Q. & Sturm, J.F. & Zhang, S., 1998. "Conic convex programming and self-dual embedding," Econometric Institute Research Papers EI 9815, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Arjan B. Berkelaar & Jos F. Sturm & Shuzhong Zhang, 1997. "Polynomial Primal-Dual Cone Affine Scaling for Semidefinite Programming," Tinbergen Institute Discussion Papers 97-025/4, Tinbergen Institute.
    3. F. A. Potra & R. Sheng, 1998. "Superlinear Convergence of Interior-Point Algorithms for Semidefinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 99(1), pages 103-119, October.
    4. A. D'Aspremont, 2003. "Interest rate model calibration using semidefinite Programming," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(3), pages 183-213.
    5. Sturm, J.F., 2001. "Avoiding Numerical Cancellation in the Interior Point Method for Solving Semidefinite Programs," Discussion Paper 2001-27, Tilburg University, Center for Economic Research.
    6. NESTEROV, Yu., 2006. "Towards nonsymmetric conic optimization," LIDAM Discussion Papers CORE 2006028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Alemseged Weldeyesus & Mathias Stolpe, 2015. "A primal-dual interior point method for large-scale free material optimization," Computational Optimization and Applications, Springer, vol. 61(2), pages 409-435, June.
    8. Ali Mohammad-Nezhad & Tamás Terlaky, 2017. "A polynomial primal-dual affine scaling algorithm for symmetric conic optimization," Computational Optimization and Applications, Springer, vol. 66(3), pages 577-600, April.
    9. Luo, Z-Q. & Sturm, J.F. & Zhang, S., 1997. "Duality Results for Conic Convex Programming," Econometric Institute Research Papers EI 9719/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    10. Gu, G. & Zangiabadi, M. & Roos, C., 2011. "Full Nesterov-Todd step infeasible interior-point method for symmetric optimization," European Journal of Operational Research, Elsevier, vol. 214(3), pages 473-484, November.
    11. Luo, Z-Q. & Sturm, J.F. & Zhang, S., 1996. "Superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming," Econometric Institute Research Papers 9607/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Sturm, J.F., 2002. "Implementation of Interior Point Methods for Mixed Semidefinite and Second Order Cone Optimization Problems," Discussion Paper 2002-73, Tilburg University, Center for Economic Research.
    13. NESTEROV, Yu., 2006. "Nonsymmetric potential-reduction methods for general cones," LIDAM Discussion Papers CORE 2006034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. de Klerk, E. & Peng, J. & Roos, C. & Terlaky, T., 2001. "A scaled Gauss-Newton primal-dual search direction for semidefinite optimization," Other publications TiSEM 9d85401c-e9d8-45ee-be2d-2, Tilburg University, School of Economics and Management.
    15. Berkelaar, A.B. & Sturm, J.F. & Zhang, S., 1996. "Polynomial Primal-Dual Cone Affine Scaling for Semidefinite Programming," Econometric Institute Research Papers EI 9667-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    16. Helmberg, C., 2002. "Semidefinite programming," European Journal of Operational Research, Elsevier, vol. 137(3), pages 461-482, March.

    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:56:y:2013:i:1:p:81-96. 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.