IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v186y2020i3d10.1007_s10957-020-01720-y.html
   My bibliography  Save this article

Superlinear Convergence of the Sequential Quadratic Method in Constrained Optimization

Author

Listed:
  • Ashkan Mohammadi

    (Wayne State University)

  • Boris S. Mordukhovich

    (Wayne State University)

  • M. Ebrahim Sarabi

    (Miami University)

Abstract

This paper pursues a twofold goal. Firstly, we aim at deriving novel second-order characterizations of important robust stability properties of perturbed Karush–Kuhn–Tucker systems for a broad class of constrained optimization problems generated by parabolically regular sets. Secondly, the obtained characterizations are applied to establish well-posedness and superlinear convergence of the basic sequential quadratic programming method to solve parabolically regular constrained optimization problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:3:d:10.1007_s10957-020-01720-y
    DOI: 10.1007/s10957-020-01720-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-020-01720-y
    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/s10957-020-01720-y?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. J. J. Ye & X. Y. Ye, 1997. "Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints," Mathematics of Operations Research, INFORMS, vol. 22(4), pages 977-997, November.
    2. 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.
    3. Yun Wang & Liwei Zhang, 2009. "Properties of equation reformulation of the Karush–Kuhn–Tucker condition for nonlinear second order cone optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(2), pages 195-218, October.
    4. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
    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. Nguyen T. V. Hang & Boris S. Mordukhovich & M. Ebrahim Sarabi, 2022. "Augmented Lagrangian method for second-order cone programs under second-order sufficiency," Journal of Global Optimization, Springer, vol. 82(1), pages 51-81, January.

    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. J. V. Outrata, 1999. "Optimality Conditions for a Class of Mathematical Programs with Equilibrium Constraints," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 627-644, August.
    2. Jin Zhang & Xide Zhu, 2022. "Linear Convergence of Prox-SVRG Method for Separable Non-smooth Convex Optimization Problems under Bounded Metric Subregularity," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 564-597, February.
    3. Lei Guo & Gui-Hua Lin & Jane J. Ye, 2013. "Second-Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 33-64, July.
    4. Yong-Jin Liu & Li Wang, 2016. "Properties associated with the epigraph of the $$l_1$$ l 1 norm function of projection onto the nonnegative orthant," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 205-221, August.
    5. M. Durea & R. Strugariu, 2011. "On parametric vector optimization via metric regularity of constraint systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 409-425, December.
    6. Liwei Zhang & Shengzhe Gao & Saoyan Guo, 2019. "Statistical Inference of Second-Order Cone Programming," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(02), pages 1-17, April.
    7. Gui-Hua Lin & Mei-Ju Luo & Jin Zhang, 2016. "Smoothing and SAA method for stochastic programming problems with non-smooth objective and constraints," Journal of Global Optimization, Springer, vol. 66(3), pages 487-510, November.
    8. Lei Guo & Gui-Hua Lin & Jane J. Ye, 2015. "Solving Mathematical Programs with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 234-256, July.
    9. Fabiana R. Oliveira & Orizon P. Ferreira & Gilson N. Silva, 2019. "Newton’s method with feasible inexact projections for solving constrained generalized equations," Computational Optimization and Applications, Springer, vol. 72(1), pages 159-177, January.
    10. Nguyen Qui, 2014. "Stability for trust-region methods via generalized differentiation," Journal of Global Optimization, Springer, vol. 59(1), pages 139-164, May.
    11. Michael Patriksson & R. Tyrrell Rockafellar, 2003. "Sensitivity Analysis of Aggregated Variational Inequality Problems, with Application to Traffic Equilibria," Transportation Science, INFORMS, vol. 37(1), pages 56-68, February.
    12. S. K. Suneja & B. Kohli, 2011. "Optimality and Duality Results for Bilevel Programming Problem Using Convexifactors," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 1-19, July.
    13. A. L. Dontchev, 1998. "A Proof of the Necessity of Linear Independence Condition and Strong Second-Order Sufficient Optimality Condition for Lipschitzian Stability in Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 467-473, August.
    14. B. S. Mordukhovich & M. E. Sarabi, 2016. "Second-Order Analysis of Piecewise Linear Functions with Applications to Optimization and Stability," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 504-526, November.
    15. 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.
    16. Huynh Van Ngai & Nguyen Huu Tron & Michel Théra, 2014. "Metric Regularity of the Sum of Multifunctions and Applications," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 355-390, February.
    17. Jie Jiang & Xiaojun Chen & Zhiping Chen, 2020. "Quantitative analysis for a class of two-stage stochastic linear variational inequality problems," Computational Optimization and Applications, Springer, vol. 76(2), pages 431-460, June.
    18. Birbil, S.I. & Gürkan, G. & Listeş, O., 2004. "Simulation-based solution of stochastic mathematical programs with complementarity constraints: Sample-path analysis," ERIM Report Series Research in Management ERS-2004-016-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    19. A. F. Izmailov & M. V. Solodov, 2023. "Convergence rate estimates for penalty methods revisited," Computational Optimization and Applications, Springer, vol. 85(3), pages 973-992, July.
    20. B. S. Mordukhovich & M. E. Sarabi, 2017. "Stability Analysis for Composite Optimization Problems and Parametric Variational Systems," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 554-577, February.

    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:186:y:2020:i:3:d:10.1007_s10957-020-01720-y. 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.