IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v67y2017i1d10.1007_s10589-016-9890-5.html
   My bibliography  Save this article

Subspace-stabilized sequential quadratic programming

Author

Listed:
  • A. F. Izmailov

    (Lomonosov Moscow State University, MSU
    RUDN University)

  • E. I. Uskov

    (Derzhavin Tambov State University, TSU)

Abstract

The stabilized sequential quadratic programming (SQP) method has nice local convergence properties: it possesses local superlinear convergence under very mild assumptions not including any constraint qualifications. However, any attempts to globalize convergence of this method indispensably face some principal difficulties concerned with intrinsic deficiencies of the steps produced by it when relatively far from solutions; specifically, it has a tendency to produce long sequences of short steps before entering the region where its superlinear convergence shows up. In this paper, we propose a modification of the stabilized SQP method, possessing better “semi-local” behavior, and hence, more suitable for the development of practical realizations. The key features of the new method are identification of the so-called degeneracy subspace and dual stabilization along this subspace only; thus the name “subspace-stabilized SQP”. We consider two versions of this method, their local convergence properties, as well as a practical procedure for approximation of the degeneracy subspace. Even though we do not consider here any specific algorithms with theoretically justified global convergence properties, subspace-stabilized SQP can be a relevant substitute for the stabilized SQP in such algorithms using the latter at the “local phase”. Some numerical results demonstrate that stabilization along the degeneracy subspace is indeed crucially important for success of dual stabilization methods.

Suggested Citation

  • A. F. Izmailov & E. I. Uskov, 2017. "Subspace-stabilized sequential quadratic programming," Computational Optimization and Applications, Springer, vol. 67(1), pages 129-154, May.
    • Handle: RePEc:spr:coopap:v:67:y:2017:i:1:d:10.1007_s10589-016-9890-5
    DOI: 10.1007/s10589-016-9890-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-016-9890-5
    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/s10589-016-9890-5?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. Boris Mordukhovich, 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 35-42, April.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Philip Gill & Daniel Robinson, 2012. "A primal-dual augmented Lagrangian," Computational Optimization and Applications, Springer, vol. 51(1), pages 1-25, January.
    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.
    9. 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.
    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. 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.

    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. 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.
    2. 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.
    3. 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.
    4. Oliver Stein & Nathan Sudermann-Merx, 2016. "The Cone Condition and Nonsmoothness in Linear Generalized Nash Games," Journal of Optimization Theory and Applications, Springer, vol. 170(2), pages 687-709, August.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Tianlei Zang & Zhengyou He & Yan Wang & Ling Fu & Zhiyu Peng & Qingquan Qian, 2017. "A Piecewise Bound Constrained Optimization for Harmonic Responsibilities Assessment under Utility Harmonic Impedance Changes," Energies, MDPI, vol. 10(7), pages 1-20, July.
    11. 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.
    12. 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.
    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. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Francisco J. Aragón Artacho & Rubén Campoy & Veit Elser, 2020. "An enhanced formulation for solving graph coloring problems with the Douglas–Rachford algorithm," Journal of Global Optimization, Springer, vol. 77(2), pages 383-403, June.
    19. 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.
    20. 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.

    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:67:y:2017:i:1:d:10.1007_s10589-016-9890-5. 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.