IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v66y2017i2d10.1007_s10589-016-9863-8.html
   My bibliography  Save this article

Fast algorithm for singly linearly constrained quadratic programs with box-like constraints

Author

Listed:
  • Meijiao Liu

    (Shenyang Aerospace University)

  • Yong-Jin Liu

    (Shenyang Aerospace University)

Abstract

This paper focuses on a singly linearly constrained class of convex quadratic programs with box-like constraints. We propose a new fast algorithm based on parametric approach and secant approximation method to solve this class of quadratic problems. We design efficient implementations for our proposed algorithm and compare its performance with two state-of-the-art standard solvers called Gurobi and Mosek. Numerical results on a variety of test problems demonstrate that our algorithm is able to efficiently solve the large-scale problems with the dimension up to fifty million and it substantially outperforms Gurobi and Mosek in terms of the running time.

Suggested Citation

  • Meijiao Liu & Yong-Jin Liu, 2017. "Fast algorithm for singly linearly constrained quadratic programs with box-like constraints," Computational Optimization and Applications, Springer, vol. 66(2), pages 309-326, March.
    • Handle: RePEc:spr:coopap:v:66:y:2017:i:2:d:10.1007_s10589-016-9863-8
    DOI: 10.1007/s10589-016-9863-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-016-9863-8
    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/s10589-016-9863-8?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. K. C. Kiwiel, 2008. "Variable Fixing Algorithms for the Continuous Quadratic Knapsack Problem," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 445-458, March.
    2. Gabriel R. Bitran & Arnoldo C. Hax, 1981. "Disaggregation and Resource Allocation Using Convex Knapsack Problems with Bounded Variables," Management Science, INFORMS, vol. 27(4), pages 431-441, April.
    3. Steven Cosares & Dorit S. Hochbaum, 1994. "Strongly Polynomial Algorithms for the Quadratic Transportation Problem with a Fixed Number of Sources," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 94-111, February.
    4. K. C. Kiwiel, 2007. "On Linear-Time Algorithms for the Continuous Quadratic Knapsack Problem," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 549-554, September.
    Full references (including those not matched with items on IDEAS)

    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. K. C. Kiwiel, 2008. "Variable Fixing Algorithms for the Continuous Quadratic Knapsack Problem," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 445-458, March.
    2. Hoto, R.S.V. & Matioli, L.C. & Santos, P.S.M., 2020. "A penalty algorithm for solving convex separable knapsack problems," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    3. Martijn H. H. Schoot Uiterkamp & Marco E. T. Gerards & Johann L. Hurink, 2022. "On a Reduction for a Class of Resource Allocation Problems," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1387-1402, May.
    4. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    5. Patriksson, Michael & Strömberg, Christoffer, 2015. "Algorithms for the continuous nonlinear resource allocation problem—New implementations and numerical studies," European Journal of Operational Research, Elsevier, vol. 243(3), pages 703-722.
    6. Hsin-Min Sun & Ruey-Lin Sheu, 2019. "Minimum variance allocation among constrained intervals," Journal of Global Optimization, Springer, vol. 74(1), pages 21-44, May.
    7. Hezhi Luo & Xianye Zhang & Huixian Wu & Weiqiang Xu, 2023. "Effective algorithms for separable nonconvex quadratic programming with one quadratic and box constraints," Computational Optimization and Applications, Springer, vol. 86(1), pages 199-240, September.
    8. Zhang, Jianzhong & Xu, Chengxian, 2010. "Inverse optimization for linearly constrained convex separable programming problems," European Journal of Operational Research, Elsevier, vol. 200(3), pages 671-679, February.
    9. Mohammadivojdan, Roshanak & Geunes, Joseph, 2018. "The newsvendor problem with capacitated suppliers and quantity discounts," European Journal of Operational Research, Elsevier, vol. 271(1), pages 109-119.
    10. Walter, Rico & Boysen, Nils & Scholl, Armin, 2013. "The discrete forward–reserve problem – Allocating space, selecting products, and area sizing in forward order picking," European Journal of Operational Research, Elsevier, vol. 229(3), pages 585-594.
    11. AgralI, Semra & Geunes, Joseph, 2009. "Solving knapsack problems with S-curve return functions," European Journal of Operational Research, Elsevier, vol. 193(2), pages 605-615, March.
    12. Lee, Zu-Hsu & Deng, Shiming & Lin, Beixin & Yang, James G.S., 2010. "Decision model and analysis for investment interest expense deduction and allocation," European Journal of Operational Research, Elsevier, vol. 200(1), pages 268-280, January.
    13. Chunli Liu & Jianjun Gao, 2015. "A polynomial case of convex integer quadratic programming problems with box integer constraints," Journal of Global Optimization, Springer, vol. 62(4), pages 661-674, August.
    14. Paul Tseng & Sangwoon Yun, 2010. "A coordinate gradient descent method for linearly constrained smooth optimization and support vector machines training," Computational Optimization and Applications, Springer, vol. 47(2), pages 179-206, October.
    15. Ion Necoara & Andrei Patrascu, 2014. "A random coordinate descent algorithm for optimization problems with composite objective function and linear coupled constraints," Computational Optimization and Applications, Springer, vol. 57(2), pages 307-337, March.
    16. Debels, D. & Vanhoucke, M., 2006. "A finite capacity production scheduling procedure for a belgian steel company," Vlerick Leuven Gent Management School Working Paper Series 2006-41, Vlerick Leuven Gent Management School.
    17. Muralidharan S. Kodialam & Hanan Luss, 1998. "Algorithms for Separable Nonlinear Resource Allocation Problems," Operations Research, INFORMS, vol. 46(2), pages 272-284, April.
    18. Bretthauer, Kurt M. & Ross, Anthony & Shetty, Bala, 1999. "Nonlinear integer programming for optimal allocation in stratified sampling," European Journal of Operational Research, Elsevier, vol. 116(3), pages 667-680, August.
    19. Amir Beck & Nadav Hallak, 2016. "On the Minimization Over Sparse Symmetric Sets: Projections, Optimality Conditions, and Algorithms," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 196-223, February.
    20. P. Tseng & S. Yun, 2009. "Block-Coordinate Gradient Descent Method for Linearly Constrained Nonsmooth Separable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 513-535, March.

    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:66:y:2017:i:2:d:10.1007_s10589-016-9863-8. 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.