IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v160y2014i1d10.1007_s10957-013-0339-z.html
   My bibliography  Save this article

Simple Sequential Quadratically Constrained Quadratic Programming Feasible Algorithm with Active Identification Sets for Constrained Minimax Problems

Author

Listed:
  • Jin-bao Jian

    (Yulin Normal University)

  • Xing-de Mo

    (Guangxi University)

  • Li-juan Qiu

    (Guangxi University)

  • Su-ming Yang

    (Guangxi Technological College of Machinery and Electricity)

  • Fu-sheng Wang

    (Taiyan Normal University)

Abstract

In this paper, the nonlinear minimax problems with inequality constraints are discussed. Based on the idea of simple sequential quadratically constrained quadratic programming algorithm for smooth constrained optimization, an alternative algorithm for solving the discussed problems is proposed. Unlike the previous work, at each iteration, a feasible direction of descent called main search direction is obtained by solving only one subprogram which is composed of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the constrained functions. Then a high-order correction direction used to avoid the Maratos effect is computed by updating the main search direction with a system of linear equations. The proposed algorithm possesses global convergence under weak Mangasarian–Fromovitz constraint qualification and superlinear convergence under suitable conditions with the upper-level strict complementarity. At last, some preliminary numerical results are reported.

Suggested Citation

  • Jin-bao Jian & Xing-de Mo & Li-juan Qiu & Su-ming Yang & Fu-sheng Wang, 2014. "Simple Sequential Quadratically Constrained Quadratic Programming Feasible Algorithm with Active Identification Sets for Constrained Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 158-188, January.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:1:d:10.1007_s10957-013-0339-z
    DOI: 10.1007/s10957-013-0339-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-013-0339-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/s10957-013-0339-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. J. B. Jian, 2006. "New Sequential Quadratically-Constrained Quadratic Programming Method of Feasible Directions and Its Convergence Rate," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 109-130, April.
    2. E. Obasanjo & G. Tzallas-Regas & B. Rustem, 2010. "An Interior-Point Algorithm for Nonlinear Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 291-318, February.
    3. M. V. Solodov, 2004. "On the Sequential Quadratically Constrained Quadratic Programming Methods," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 64-79, February.
    4. Jian, Jin-Bao & Tang, Chun-Ming & Zheng, Hai-Yan, 2010. "Sequential quadratically constrained quadratic programming norm-relaxed algorithm of strongly sub-feasible directions," European Journal of Operational Research, Elsevier, vol. 200(3), pages 645-657, February.
    5. E. Polak & R. S. Womersley & H. X. Yin, 2008. "An Algorithm Based on Active Sets and Smoothing for Discretized Semi-Infinite Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 311-328, August.
    6. Fusheng Wang & Kecun Zhang, 2008. "A hybrid algorithm for nonlinear minimax problems," Annals of Operations Research, Springer, vol. 164(1), pages 167-191, 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. Li, Jianling & Yang, Zhenping, 2018. "A QP-free algorithm without a penalty function or a filter for nonlinear general-constrained optimization," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 52-72.

    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. Jian, Jin-Bao & Pan, Hua-Qin & Tang, Chun-Ming & Li, Jian-Ling, 2015. "A strongly sub-feasible primal-dual quasi interior-point algorithm for nonlinear inequality constrained optimization," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 560-578.
    2. E. Y. Pee & J. O. Royset, 2011. "On Solving Large-Scale Finite Minimax Problems Using Exponential Smoothing," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 390-421, February.
    3. Li, Jianling & Yang, Zhenping, 2018. "A QP-free algorithm without a penalty function or a filter for nonlinear general-constrained optimization," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 52-72.
    4. Tang, Chun-ming & Jian, Jin-bao, 2012. "Strongly sub-feasible direction method for constrained optimization problems with nonsmooth objective functions," European Journal of Operational Research, Elsevier, vol. 218(1), pages 28-37.
    5. Junxiang Li & Mingsong Cheng & Bo Yu & Shuting Zhang, 2015. "Group Update Method for Sparse Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(1), pages 257-277, July.
    6. Jian, Jin-Bao & Tang, Chun-Ming & Zheng, Hai-Yan, 2010. "Sequential quadratically constrained quadratic programming norm-relaxed algorithm of strongly sub-feasible directions," European Journal of Operational Research, Elsevier, vol. 200(3), pages 645-657, February.
    7. Zhengyong Zhou & Xiaoyang Dai, 2023. "An active set strategy to address the ill-conditioning of smoothing methods for solving finite linear minimax problems," Journal of Global Optimization, Springer, vol. 85(2), pages 421-439, February.
    8. Alfred Auslender, 2013. "An Extended Sequential Quadratically Constrained Quadratic Programming Algorithm for Nonlinear, Semidefinite, and Second-Order Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 183-212, February.
    9. 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.
    10. Fusheng Wang, 2013. "A hybrid algorithm for linearly constrained minimax problems," Annals of Operations Research, Springer, vol. 206(1), pages 501-525, July.
    11. Jérôme Bolte & Edouard Pauwels, 2016. "Majorization-Minimization Procedures and Convergence of SQP Methods for Semi-Algebraic and Tame Programs," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 442-465, May.
    12. Jin-bao Jian & Qing-juan Hu & Chun-ming Tang, 2014. "Superlinearly Convergent Norm-Relaxed SQP Method Based on Active Set Identification and New Line Search for Constrained Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 859-883, December.
    13. J. O. Royset & E. Y. Pee, 2012. "Rate of Convergence Analysis of Discretization and Smoothing Algorithms for Semiinfinite Minimax Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 855-882, December.
    14. Francisco Facchinei & Vyacheslav Kungurtsev & Lorenzo Lampariello & Gesualdo Scutari, 2021. "Ghost Penalties in Nonconvex Constrained Optimization: Diminishing Stepsizes and Iteration Complexity," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 595-627, May.
    15. A. Izmailov & M. Solodov, 2010. "Inexact Josephy–Newton framework for generalized equations and its applications to local analysis of Newtonian methods for constrained optimization," Computational Optimization and Applications, Springer, vol. 46(2), pages 347-368, June.
    16. Fusheng Wang & Kecun Zhang, 2008. "A hybrid algorithm for nonlinear minimax problems," Annals of Operations Research, Springer, vol. 164(1), pages 167-191, November.
    17. H. Chung & E. Polak & S. Sastry, 2010. "On the Use of Outer Approximations as an External Active Set Strategy," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 51-75, July.
    18. Tao-Wen Liu, 2011. "A reduced Hessian SQP method for inequality constrained optimization," Computational Optimization and Applications, Springer, vol. 49(1), pages 31-59, May.
    19. Mohammad Ali Abooshahab & Mohsen Ekramian & Mohammad Ataei & Ali Ebrahimpour-Boroojeny, 2019. "Time-Delay Estimation in State and Output Equations of Nonlinear Systems Using Optimal Computational Approach," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 1036-1064, March.
    20. Van-Bong Nguyen & Thi Ngan Nguyen & Ruey-Lin Sheu, 2020. "Strong duality in minimizing a quadratic form subject to two homogeneous quadratic inequalities over the unit sphere," Journal of Global Optimization, Springer, vol. 76(1), pages 121-135, January.

    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:160:y:2014:i:1:d:10.1007_s10957-013-0339-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.