IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v96y1998i1d10.1023_a1022663100715.html
   My bibliography  Save this article

Inexact Interior-Point Method

Author

Listed:
  • S. Bellavia

    (Università di Padova)

Abstract

In this paper, we introduce an inexact interior-point algorithm for a constrained system of equations. The formulation of the problem is quite general and includes nonlinear complementarity problems of various kinds. In our convergence theory, we interpret the inexact interior-point method as an inexact Newton method. This enables us to establish a global convergence theory for the proposed algorithm. Under the additional assumption of the invertibility of the Jacobian at the solution, the superlinear convergence of the iteration sequence is proved.

Suggested Citation

  • S. Bellavia, 1998. "Inexact Interior-Point Method," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 109-121, January.
    • Handle: RePEc:spr:joptap:v:96:y:1998:i:1:d:10.1023_a:1022663100715
    DOI: 10.1023/A:1022663100715
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022663100715
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1022663100715?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. Stephen Wright & Daniel Ralph, 1996. "A Superlinear Infeasible-Interior-Point Algorithm for Monotone Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 815-838, November.
    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. Gondzio, Jacek, 2016. "Crash start of interior point methods," European Journal of Operational Research, Elsevier, vol. 255(1), pages 308-314.
    2. Gondzio, Jacek, 2012. "Interior point methods 25 years later," European Journal of Operational Research, Elsevier, vol. 218(3), pages 587-601.
    3. Jacek Gondzio, 2012. "Matrix-free interior point method," Computational Optimization and Applications, Springer, vol. 51(2), pages 457-480, March.
    4. C. Durazzi, 2000. "On the Newton Interior-Point Method for Nonlinear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 73-90, January.
    5. Benedetta Morini & Valeria Simoncini, 2017. "Stability and Accuracy of Inexact Interior Point Methods for Convex Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 450-477, November.
    6. G. Al-Jeiroudi & J. Gondzio, 2009. "Convergence Analysis of the Inexact Infeasible Interior-Point Method for Linear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 231-247, May.
    7. Paul Armand & Joël Benoist & Jean-Pierre Dussault, 2012. "Local path-following property of inexact interior methods in nonlinear programming," Computational Optimization and Applications, Springer, vol. 52(1), pages 209-238, May.
    8. Benedetta Morini & Valeria Simoncini & Mattia Tani, 2017. "A comparison of reduced and unreduced KKT systems arising from interior point methods," Computational Optimization and Applications, Springer, vol. 68(1), pages 1-27, September.
    9. Dominik Garmatter & Margherita Porcelli & Francesco Rinaldi & Martin Stoll, 2023. "An improved penalty algorithm using model order reduction for MIPDECO problems with partial observations," Computational Optimization and Applications, Springer, vol. 84(1), pages 191-223, January.
    10. David Ek & Anders Forsgren, 2023. "A structured modified Newton approach for solving systems of nonlinear equations arising in interior-point methods for quadratic programming," Computational Optimization and Applications, Springer, vol. 86(1), pages 1-48, September.
    11. Md Sarowar Morshed & Md Saiful Islam & Md. Noor-E-Alam, 2020. "Accelerated sampling Kaczmarz Motzkin algorithm for the linear feasibility problem," Journal of Global Optimization, Springer, vol. 77(2), pages 361-382, June.
    12. C. Durazzi & V. Ruggiero & G. Zanghirati, 2001. "Parallel Interior-Point Method for Linear and Quadratic Programs with Special Structure," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 289-313, August.
    13. Stefania Bellavia & Valentina De Simone & Daniela di Serafino & Benedetta Morini, 2016. "On the update of constraint preconditioners for regularized KKT systems," Computational Optimization and Applications, Springer, vol. 65(2), pages 339-360, November.

    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. Zhi-Long Dong & Fengmin Xu & Yu-Hong Dai, 2020. "Fast algorithms for sparse portfolio selection considering industries and investment styles," Journal of Global Optimization, Springer, vol. 78(4), pages 763-789, December.
    2. J. Sun & G. Y. Zhao, 1998. "Quadratic Convergence of a Long-Step Interior-Point Method for Nonlinear Monotone Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 471-491, May.
    3. R. Andreani & C. E. Echagüe & M. L. Schuverdt, 2010. "Constant-Rank Condition and Second-Order Constraint Qualification," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 255-266, August.

    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:joptap:v:96:y:1998:i:1:d:10.1023_a:1022663100715. 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.