IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v62y2015i2p405-429.html
   My bibliography  Save this article

Combining stabilized SQP with the augmented Lagrangian algorithm

Author

Listed:
  • A. Izmailov
  • M. Solodov
  • E. Uskov

Abstract

For an optimization problem with general equality and inequality constraints, we propose an algorithm which uses subproblems of the stabilized SQP (sSQP) type for approximately solving subproblems of the augmented Lagrangian method. The motivation is to take advantage of the well-known robust behavior of the augmented Lagrangian algorithm, including on problems with degenerate constraints, and at the same time try to reduce the overall algorithm locally to sSQP (which gives fast local convergence rate under weak assumptions). Specifically, the algorithm first verifies whether the primal-dual sSQP step (with unit stepsize) makes good progress towards decreasing the violation of optimality conditions for the original problem, and if so, makes this step. Otherwise, the primal part of the sSQP direction is used for linesearch that decreases the augmented Lagrangian, keeping the multiplier estimate fixed for the time being. The overall algorithm has reasonable global convergence guarantees, and inherits strong local convergence rate properties of sSQP under the same weak assumptions. Numerical results on degenerate problems and comparisons with some alternatives are reported. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • A. Izmailov & M. Solodov & E. Uskov, 2015. "Combining stabilized SQP with the augmented Lagrangian algorithm," Computational Optimization and Applications, Springer, vol. 62(2), pages 405-429, November.
    • Handle: RePEc:spr:coopap:v:62:y:2015:i:2:p:405-429
    DOI: 10.1007/s10589-015-9744-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-015-9744-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-015-9744-6?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. A. F. Izmailov & M. V. Solodov, 2015. "Newton-Type Methods: A Broader View," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 577-620, February.
    2. D. Fernández & E. Pilotta & G. Torres, 2013. "An inexact restoration strategy for the globalization of the sSQP method," Computational Optimization and Applications, Springer, vol. 54(3), pages 595-617, April.
    3. A. Izmailov & M. Solodov, 2009. "Examples of dual behaviour of Newton-type methods on optimization problems with degenerate constraints," Computational Optimization and Applications, Springer, vol. 42(2), pages 231-264, March.
    4. Philip Gill & Daniel Robinson, 2012. "A primal-dual augmented Lagrangian," Computational Optimization and Applications, Springer, vol. 51(1), pages 1-25, January.
    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. A. F. Izmailov & M. V. Solodov & E. I. Uskov, 2019. "A globally convergent Levenberg–Marquardt method for equality-constrained optimization," Computational Optimization and Applications, Springer, vol. 72(1), pages 215-239, January.
    3. E. G. Birgin & R. D. Lobato & J. M. Martínez, 2017. "A nonlinear programming model with implicit variables for packing ellipsoids," Journal of Global Optimization, Springer, vol. 68(3), pages 467-499, July.
    4. A. F. Izmailov, 2021. "Accelerating convergence of a globalized sequential quadratic programming method to critical Lagrange multipliers," Computational Optimization and Applications, Springer, vol. 80(3), pages 943-978, December.
    5. E. G. Birgin & R. D. Lobato & J. M. Martínez, 2016. "Packing ellipsoids by nonlinear optimization," Journal of Global Optimization, Springer, vol. 65(4), pages 709-743, August.
    6. 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.
    7. A. F. Izmailov & E. I. Uskov, 2017. "Subspace-stabilized sequential quadratic programming," Computational Optimization and Applications, Springer, vol. 67(1), pages 129-154, May.
    8. A. F. Izmailov & M. V. Solodov & E. I. Uskov, 2016. "Globalizing Stabilized Sequential Quadratic Programming Method by Smooth Primal-Dual Exact Penalty Function," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 148-178, April.

    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. A. Izmailov & M. Solodov, 2015. "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 1-26, April.
    2. A. F. Izmailov & E. I. Uskov, 2017. "Subspace-stabilized sequential quadratic programming," Computational Optimization and Applications, Springer, vol. 67(1), pages 129-154, May.
    3. A. F. Izmailov & M. V. Solodov & E. I. Uskov, 2016. "Globalizing Stabilized Sequential Quadratic Programming Method by Smooth Primal-Dual Exact Penalty Function," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 148-178, April.
    4. Daniel Robinson, 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 43-47, April.
    5. A. F. Izmailov & M. V. Solodov, 2015. "Newton-Type Methods: A Broader View," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 577-620, February.
    6. A. Izmailov & M. Solodov, 2015. "Rejoinder 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 48-52, April.
    7. Ashkan Mohammadi & Boris S. Mordukhovich & M. Ebrahim Sarabi, 2020. "Superlinear Convergence of the Sequential Quadratic Method in Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 731-758, September.
    8. A. F. Izmailov & M. V. Solodov, 2022. "Perturbed Augmented Lagrangian Method Framework with Applications to Proximal and Smoothed Variants," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 491-522, June.
    9. A. F. Izmailov & M. V. Solodov & E. I. Uskov, 2019. "A globally convergent Levenberg–Marquardt method for equality-constrained optimization," Computational Optimization and Applications, Springer, vol. 72(1), pages 215-239, January.
    10. 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.
    11. 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.
    12. Adrian S. Lewis & Calvin Wylie, 2021. "Active‐Set Newton Methods and Partial Smoothness," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 712-725, May.
    13. 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.
    14. Daniel P. Robinson, 2015. "Primal-Dual Active-Set Methods for Large-Scale Optimization," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 137-171, July.
    15. Songqiang Qiu, 2019. "Convergence of a stabilized SQP method for equality constrained optimization," Computational Optimization and Applications, Springer, vol. 73(3), pages 957-996, July.
    16. A. Izmailov & A. Kurennoy & M. Solodov, 2015. "Local convergence of the method of multipliers for variational and optimization problems under the noncriticality assumption," Computational Optimization and Applications, Springer, vol. 60(1), pages 111-140, January.
    17. Welington Oliveira, 2020. "Sequential Difference-of-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 936-959, September.
    18. 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.

    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:62:y:2015:i:2:p:405-429. 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.