IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v65y2016i4d10.1007_s10898-015-0400-6.html
   My bibliography  Save this article

A stabilized filter SQP algorithm for nonlinear programming

Author

Listed:
  • Chungen Shen

    (University of Shanghai for Science and Technology)

  • Lei-Hong Zhang

    (Shanghai University of Finance and Economics
    Shanghai Key Laboratory of Financial Information Technology (Shanghai University of Finance and Economics))

  • Wei Liu

    (Shanghai Key Laboratory of Financial Information Technology (Shanghai University of Finance and Economics)
    Shanghai Finance University)

Abstract

This paper presents a stabilized filter sequential quadratic programming (SQP) method for the general nonlinear optimization problems. The technique of stabilizing the inner quadratic programmings is an efficient strategy for the degenerate problem and brings the local superlinear convergence, while the integrated filter technique works effectively and guarantees the global convergence. The new algorithm works on both the primal and dual variables and solves the problem within the computational complexity comparable to the classical SQP algorithm. For the convergence, we show that (1) it converges either to a Karush–Kuhn–Tucker point at which the cone-continuity property holds, or to a stationary point in the sense of minimizing the constraint violation, and (2) under some second-order sufficient conditions, it converges locally superlinearly without any constraint qualifications. Our preliminary numerical results on a set of CUTEr test problems as well as on degenerate problems demonstrate the efficiency of the new algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:65:y:2016:i:4:d:10.1007_s10898-015-0400-6
    DOI: 10.1007/s10898-015-0400-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-015-0400-6
    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/s10898-015-0400-6?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. R. Andreani & J. M. Martinez & M. L. Schuverdt, 2005. "On the Relation between Constant Positive Linear Dependence Condition and Quasinormality Constraint Qualification," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 473-483, May.
    2. 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.
    3. 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.
    4. Chungen Shen & Sven Leyffer & Roger Fletcher, 2012. "A nonmonotone filter method for nonlinear optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 583-607, July.
    5. Zsolt Ugray & Leon Lasdon & John Plummer & Fred Glover & James Kelly & Rafael Martí, 2007. "Scatter Search and Local NLP Solvers: A Multistart Framework for Global Optimization," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 328-340, August.
    6. 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.
    7. Joseph Frédéric Bonnans & Alexander Ioffe, 1995. "Second-order Sufficiency and Quadratic Growth for Nonisolated Minima," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 801-817, 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. 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.
    2. 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. Chungen Shen & Lei-Hong Zhang & Bo Wang & Wenqiong Shao, 2014. "Global and local convergence of a nonmonotone SQP method for constrained nonlinear optimization," Computational Optimization and Applications, Springer, vol. 59(3), pages 435-473, December.
    2. 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.
    3. 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.
    4. Xu Wang & Jingni Song & Qunqi Wu, 2021. "An Economic Equilibrium Model for Optimizing Passenger Transport Corridor Mode Structure Based on Travel Surplus," Sustainability, MDPI, vol. 13(7), pages 1-18, April.
    5. Giorgio, 2019. "On Second-Order Optimality Conditions in Smooth Nonlinear Programming Problems," DEM Working Papers Series 171, University of Pavia, Department of Economics and Management.
    6. Zilong, Ti & Xiao Wei, Deng, 2022. "Layout optimization of offshore wind farm considering spatially inhomogeneous wave loads," Applied Energy, Elsevier, vol. 306(PA).
    7. L. F. Bueno & G. Haeser & J. M. Martínez, 2015. "A Flexible Inexact-Restoration Method for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 188-208, April.
    8. Kuang Bai & Yixia Song & Jin Zhang, 2023. "Second-Order Enhanced Optimality Conditions and Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1264-1284, September.
    9. Dionisios Koutsantonis & Konstantinos Koutsantonis & Nikolaos P. Bakas & Vagelis Plevris & Andreas Langousis & Savvas A. Chatzichristofis, 2022. "Bibliometric Literature Review of Adaptive Learning Systems," Sustainability, MDPI, vol. 14(19), pages 1-18, October.
    10. M. Fernanda P. Costa & Ana Maria A. C. Rocha & Edite M. G. P. Fernandes, 2018. "Filter-based DIRECT method for constrained global optimization," Journal of Global Optimization, Springer, vol. 71(3), pages 517-536, July.
    11. Lingcai Kong & Jinfeng Wang & Weiguo Han & Zhidong Cao, 2016. "Modeling Heterogeneity in Direct Infectious Disease Transmission in a Compartmental Model," IJERPH, MDPI, vol. 13(3), pages 1-13, February.
    12. Zhongwen Chen & Yu-Hong Dai & Jiangyan Liu, 2020. "A penalty-free method with superlinear convergence for equality constrained optimization," Computational Optimization and Applications, Springer, vol. 76(3), pages 801-833, July.
    13. Pei, Yonggang & Zhu, Detong, 2016. "Local convergence of a trust-region algorithm with line search filter technique for nonlinear constrained optimization," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 797-808.
    14. Leonid Minchenko, 2019. "Note on Mangasarian–Fromovitz-Like Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1199-1204, September.
    15. Rommel G. Regis & Christine A. Shoemaker, 2009. "Parallel Stochastic Global Optimization Using Radial Basis Functions," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 411-426, August.
    16. L. Minchenko & A. Tarakanov, 2011. "On Error Bounds for Quasinormal Programs," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 571-579, March.
    17. Falk Lieder & Klaas E Stephan & Jean Daunizeau & Marta I Garrido & Karl J Friston, 2013. "A Neurocomputational Model of the Mismatch Negativity," PLOS Computational Biology, Public Library of Science, vol. 9(11), pages 1-14, November.
    18. Shen, Yuelin, 2018. "Pricing contracts and planning stochastic resources in brand display advertising," Omega, Elsevier, vol. 81(C), pages 183-194.
    19. Wu, Feng & Guan, Zhengfei & Whitaker, Vance, 2015. "Optimizing yield distribution under biological and economic constraints: Florida strawberries as a model for perishable commodities," Agricultural Systems, Elsevier, vol. 141(C), pages 113-120.
    20. 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.

    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:jglopt:v:65:y:2016:i:4:d:10.1007_s10898-015-0400-6. 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.