IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v206y2010i1p34-45.html
   My bibliography  Save this article

Global convergence of a robust filter SQP algorithm

Author

Listed:
  • Shen, Chungen
  • Xue, Wenjuan
  • Chen, Xiongda

Abstract

We present a robust filter SQP algorithm for solving constrained optimization problems. This algorithm is based on the modified quadratic programming proposed by Burke to avoid the infeasibility of the quadratic programming subproblem at each iteration. Compared with other filter SQP algorithms, our algorithm does not require any restoration phase procedure which may spend a large amount of computation. The main advantage of our algorithm is that it is globally convergent without requiring strong constraint qualifications, such as Mangasarian-Fromovitz constraint qualification (MFCQ) and the constant rank constraint qualification (CRCQ). Furthermore, the feasible limit points of the sequence generated by our algorithm are proven to be the KKT points if some weaker conditions are satisfied. Numerical results are also presented to show the efficiency of the algorithm.

Suggested Citation

  • Shen, Chungen & Xue, Wenjuan & Chen, Xiongda, 2010. "Global convergence of a robust filter SQP algorithm," European Journal of Operational Research, Elsevier, vol. 206(1), pages 34-45, October.
    • Handle: RePEc:eee:ejores:v:206:y:2010:i:1:p:34-45
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00162-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Jian, Jin-Bao & Xu, Qing-Juan & Han, Dao-Lan, 2008. "A norm-relaxed method of feasible directions for finely discretized problems from semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 186(1), pages 41-62, April.
    2. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    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. Trindade, Graça & Dias, José G. & Ambrósio, Jorge, 2017. "Extracting clusters from aggregate panel data: A market segmentation study," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 277-288.
    2. Trindade, Graça & Ambrósio, Jorge, 2012. "An optimization method to estimate models with store-level data: A case study," European Journal of Operational Research, Elsevier, vol. 217(3), pages 664-672.

    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. Holger Berthold & Holger Heitsch & René Henrion & Jan Schwientek, 2022. "On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 1-37, August.
    2. Peter Kirst & Oliver Stein, 2016. "Solving Disjunctive Optimization Problems by Generalized Semi-infinite Optimization Techniques," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1079-1109, June.
    3. Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
    4. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2023. "Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation," Management Science, INFORMS, vol. 69(4), pages 2051-2068, April.
    5. Li-Ping Pang & Jian Lv & Jin-He Wang, 2016. "Constrained incremental bundle method with partial inexact oracle for nonsmooth convex semi-infinite programming problems," Computational Optimization and Applications, Springer, vol. 64(2), pages 433-465, June.
    6. Tadeusz Antczak, 2022. "Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints," 4OR, Springer, vol. 20(3), pages 417-442, September.
    7. Souvik Das & Ashwin Aravind & Ashish Cherukuri & Debasish Chatterjee, 2022. "Near-optimal solutions of convex semi-infinite programs via targeted sampling," Annals of Operations Research, Springer, vol. 318(1), pages 129-146, November.
    8. Aguiar, Victor H. & Kashaev, Nail & Allen, Roy, 2023. "Prices, profits, proxies, and production," Journal of Econometrics, Elsevier, vol. 235(2), pages 666-693.
    9. Li Wang & Feng Guo, 2014. "Semidefinite relaxations for semi-infinite polynomial programming," Computational Optimization and Applications, Springer, vol. 58(1), pages 133-159, May.
    10. S. Mishra & M. Jaiswal & H. Le Thi, 2012. "Nonsmooth semi-infinite programming problem using Limiting subdifferentials," Journal of Global Optimization, Springer, vol. 53(2), pages 285-296, June.
    11. Hatim Djelassi & Alexander Mitsos, 2021. "Global Solution of Semi-infinite Programs with Existence Constraints," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 863-881, March.
    12. Ryoichi Nishimura & Shunsuke Hayashi & Masao Fukushima, 2013. "SDP reformulation for robust optimization problems based on nonconvex QP duality," Computational Optimization and Applications, Springer, vol. 55(1), pages 21-47, May.
    13. Feng Guo & Xiaoxia Sun, 2020. "On semi-infinite systems of convex polynomial inequalities and polynomial optimization problems," Computational Optimization and Applications, Springer, vol. 75(3), pages 669-699, April.
    14. Shaojian Qu & Mark Goh & Soon-Yi Wu & Robert Souza, 2014. "Multiobjective DC programs with infinite convex constraints," Journal of Global Optimization, Springer, vol. 59(1), pages 41-58, May.
    15. Cao Thanh Tinh & Thai Doan Chuong, 2022. "Conic Linear Programming Duals for Classes of Quadratic Semi-Infinite Programs with Applications," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 570-596, August.
    16. Josef Kallrath & Steffen Rebennack, 2014. "Cutting ellipses from area-minimizing rectangles," Journal of Global Optimization, Springer, vol. 59(2), pages 405-437, July.
    17. Duarte, Belmiro P.M. & Sagnol, Guillaume & Wong, Weng Kee, 2018. "An algorithm based on semidefinite programming for finding minimax optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 99-117.
    18. Steffen Rebennack & Josef Kallrath, 2015. "Continuous Piecewise Linear Delta-Approximations for Univariate Functions: Computing Minimal Breakpoint Systems," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 617-643, November.
    19. Nazih Abderrazzak Gadhi, 2019. "Necessary optimality conditions for a nonsmooth semi-infinite programming problem," Journal of Global Optimization, Springer, vol. 74(1), pages 161-168, May.
    20. He, Li & Huang, Guo H. & Lu, Hongwei, 2011. "Bivariate interval semi-infinite programming with an application to environmental decision-making analysis," European Journal of Operational Research, Elsevier, vol. 211(3), pages 452-465, 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:eee:ejores:v:206:y:2010:i:1:p:34-45. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.