IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v91y2025i3d10.1007_s10589-025-00690-z.html
   My bibliography  Save this article

Convergence analysis of a mixed logarithmic barrier-augmented Lagrangian algorithm without constraint qualification

Author

Listed:
  • Tran Ngoc Nguyen

    (Quy Nhon University)

Abstract

In this paper, we exploit some properties of points in a neighborhood of the solution set of degenerate optimization problems. Combining these facts with the boundedness of the inverse of regularized Jacobian matrix arising in a mixed logarithmic barrier-augmented lagrangian method, we propose an updating rule for parameters of a mixed logarithmic barrier-augmented Lagrangian algorithm. The superlinear convergence of this algorithm is then proved without any constraint qualification. Numerical results on degenerate problems are also presented to confirm theoretical results.

Suggested Citation

  • Tran Ngoc Nguyen, 2025. "Convergence analysis of a mixed logarithmic barrier-augmented Lagrangian algorithm without constraint qualification," Computational Optimization and Applications, Springer, vol. 91(3), pages 1105-1134, July.
    • Handle: RePEc:spr:coopap:v:91:y:2025:i:3:d:10.1007_s10589-025-00690-z
    DOI: 10.1007/s10589-025-00690-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-025-00690-z
    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/s10589-025-00690-z?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. Dominique Orban & Abel Soares Siqueira, 2020. "A regularization method for constrained nonlinear least squares," Computational Optimization and Applications, Springer, vol. 76(3), pages 961-989, July.
    2. Paul Armand & Joël Benoist & Riadh Omheni & Vincent Pateloup, 2014. "Study of a primal-dual algorithm for equality constrained minimization," Computational Optimization and Applications, Springer, vol. 59(3), pages 405-433, December.
    3. Alberto Marchi, 2022. "On a primal-dual Newton proximal method for convex quadratic programs," Computational Optimization and Applications, Springer, vol. 81(2), pages 369-395, March.
    4. Andreas Fischer, 1999. "Modified Wilson's Method for Nonlinear Programs with Nonunique Multipliers," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 699-727, August.
    5. Stephen J. Wright & Dominique Orban, 2002. "Properties of the Log-Barrier Function on Degenerate Nonlinear Programs," Mathematics of Operations Research, INFORMS, vol. 27(3), pages 585-613, August.
    6. Spyridon Pougkakiotis & Jacek Gondzio, 2021. "An interior point-proximal method of multipliers for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 78(2), pages 307-351, March.
    7. Paul Armand & Riadh Omheni, 2017. "A Mixed Logarithmic Barrier-Augmented Lagrangian Method for Nonlinear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 523-547, May.
    8. Daniel Ralph & Stephen J. Wright, 2000. "Superlinear Convergence of an Interior-Point Method Despite Dependent Constraints," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 179-194, May.
    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. Stefano Cipolla & Jacek Gondzio, 2023. "Proximal Stabilized Interior Point Methods and Low-Frequency-Update Preconditioning Techniques," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1061-1103, June.
    2. Paul Armand & Ngoc Nguyen Tran, 2019. "An Augmented Lagrangian Method for Equality Constrained Optimization with Rapid Infeasibility Detection Capabilities," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 197-215, April.
    3. Chungen Shen & Lei-Hong Zhang & Wei Liu, 2016. "A stabilized filter SQP algorithm for nonlinear programming," Journal of Global Optimization, Springer, vol. 65(4), pages 677-708, August.
    4. Jacek Gondzio & Spyridon Pougkakiotis & John W. Pearson, 2022. "General-purpose preconditioning for regularized interior point methods," Computational Optimization and Applications, Springer, vol. 83(3), pages 727-757, December.
    5. Andreas Fischer, 2015. "Comments on: Critical Lagrange multipliers: what we currently know about them, how they spoil our lives, and what we can do about it," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 27-31, April.
    6. Silvia Berra & Alessandro Torraca & Federico Benvenuto & Sara Sommariva, 2024. "Combined Newton-Gradient Method for Constrained Root-Finding in Chemical Reaction Networks," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 404-427, January.
    7. Xin Jiang & Lieven Vandenberghe, 2022. "Bregman primal–dual first-order method and application to sparse semidefinite programming," Computational Optimization and Applications, Springer, vol. 81(1), pages 127-159, January.
    8. Chuan He & Heng Huang & Zhaosong Lu, 2024. "A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimization," Computational Optimization and Applications, Springer, vol. 89(3), pages 843-894, December.
    9. Ernesto G. Birgin, 2020. "Preface of the special issue dedicated to the XII Brazilian workshop on continuous optimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 615-619, July.
    10. Paul Armand & Ngoc Nguyen Tran, 2021. "Local Convergence Analysis of a Primal–Dual Method for Bound-Constrained Optimization Without SOSC," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 96-116, April.
    11. Renke Kuhlmann & Christof Büskens, 2018. "A primal–dual augmented Lagrangian penalty-interior-point filter line search algorithm," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(3), pages 451-483, June.
    12. Biao Qu & Changyu Wang & Naihua Xiu, 2017. "Analysis on Newton projection method for the split feasibility problem," Computational Optimization and Applications, Springer, vol. 67(1), pages 175-199, May.
    13. Spyridon Pougkakiotis & Jacek Gondzio, 2021. "An interior point-proximal method of multipliers for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 78(2), pages 307-351, March.
    14. Uday V. Shanbhag & Gerd Infanger & Peter W. Glynn, 2011. "A Complementarity Framework for Forward Contracting Under Uncertainty," Operations Research, INFORMS, vol. 59(4), pages 810-834, August.
    15. Ahmadi-Javid, Amir & Fallah-Tafti, Malihe, 2019. "Portfolio optimization with entropic value-at-risk," European Journal of Operational Research, Elsevier, vol. 279(1), pages 225-241.
    16. Spyridon Pougkakiotis & Jacek Gondzio, 2022. "An Interior Point-Proximal Method of Multipliers for Linear Positive Semi-Definite Programming," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 97-129, January.
    17. Paul Armand & Riadh Omheni, 2017. "A Mixed Logarithmic Barrier-Augmented Lagrangian Method for Nonlinear Optimization," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 523-547, May.
    18. Spyridon Pougkakiotis & Jacek Gondzio, 2019. "Dynamic Non-diagonal Regularization in Interior Point Methods for Linear and Convex Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 905-945, June.
    19. Shaoze Li & Zhibin Deng & Cheng Lu & Junhao Wu & Jinyu Dai & Qiao Wang, 2023. "An efficient global algorithm for indefinite separable quadratic knapsack problems with box constraints," Computational Optimization and Applications, Springer, vol. 86(1), pages 241-273, September.
    20. Gemayqzel Bouza & Georg Still, 2007. "Mathematical Programs with Complementarity Constraints: Convergence Properties of a Smoothing Method," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 467-483, May.

    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:91:y:2025:i:3:d:10.1007_s10589-025-00690-z. 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.