IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v56y2013i4p1441-1455.html
   My bibliography  Save this article

A polynomial case of the cardinality-constrained quadratic optimization problem

Author

Listed:
  • Jianjun Gao
  • Duan Li

Abstract

We propose in this paper a fixed parameter polynomial algorithm for the cardinality-constrained quadratic optimization problem, which is NP-hard in general. More specifically, we prove that, given a problem of size n (the number of decision variables) and s (the cardinality), if the n−k largest eigenvalues of the coefficient matrix of the problem are identical for some 0 > k ≤ n, we can construct a solution algorithm with computational complexity of $${\mathcal{O}\left(n^{2k}\right)}$$ . Note that this computational complexity is independent of the cardinality s and is achieved by decomposing the primary problem into several convex subproblems, where the total number of the subproblems is determined by the cell enumeration algorithm for hyperplane arrangement in $${\mathbb{R}^k}$$ space. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Jianjun Gao & Duan Li, 2013. "A polynomial case of the cardinality-constrained quadratic optimization problem," Journal of Global Optimization, Springer, vol. 56(4), pages 1441-1455, August.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:4:p:1441-1455
    DOI: 10.1007/s10898-012-9853-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-012-9853-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-012-9853-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. Dimitris Bertsimas & Romy Shioda, 2009. "Algorithm for cardinality-constrained quadratic optimization," Computational Optimization and Applications, Springer, vol. 43(1), pages 1-22, May.
    2. Duan Li & Xiaoling Sun & Jun Wang, 2006. "Optimal Lot Solution To Cardinality Constrained Mean–Variance Formulation For Portfolio Selection," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 83-101, January.
    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. Lili Pan & Ziyan Luo & Naihua Xiu, 2017. "Restricted Robinson Constraint Qualification and Optimality for Cardinality-Constrained Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 104-118, October.
    2. 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.
    3. Kelsey Maass & Minsun Kim & Aleksandr Aravkin, 2022. "A Nonconvex Optimization Approach to IMRT Planning with Dose–Volume Constraints," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1366-1386, May.
    4. Jianjun Gao & Duan Li, 2013. "Optimal Cardinality Constrained Portfolio Selection," Operations Research, INFORMS, vol. 61(3), pages 745-761, June.

    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. Lili Pan & Ziyan Luo & Naihua Xiu, 2017. "Restricted Robinson Constraint Qualification and Optimality for Cardinality-Constrained Cone Programming," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 104-118, October.
    2. Zhi-Long Dong & Fengmin Xu & Yu-Hong Dai, 2020. "Fast algorithms for sparse portfolio selection considering industries and investment styles," Journal of Global Optimization, Springer, vol. 78(4), pages 763-789, December.
    3. Nasim Dehghan Hardoroudi & Abolfazl Keshvari & Markku Kallio & Pekka Korhonen, 2017. "Solving cardinality constrained mean-variance portfolio problems via MILP," Annals of Operations Research, Springer, vol. 254(1), pages 47-59, July.
    4. E. Grizickas Sapkute & M. A. Sánchez-Granero & M. N. López García & J. E. Trinidad Segovia, 2022. "The impact of regulation-based constraints on portfolio selection: The Spanish case," Palgrave Communications, Palgrave Macmillan, vol. 9(1), pages 1-14, December.
    5. Adolfo Hilario-Caballero & Ana Garcia-Bernabeu & Jose Vicente Salcedo & Marisa Vercher, 2020. "Tri-Criterion Model for Constructing Low-Carbon Mutual Fund Portfolios: A Preference-Based Multi-Objective Genetic Algorithm Approach," IJERPH, MDPI, vol. 17(17), pages 1-15, August.
    6. Xiaojin Zheng & Xiaoling Sun & Duan Li & Jie Sun, 2014. "Successive convex approximations to cardinality-constrained convex programs: a piecewise-linear DC approach," Computational Optimization and Applications, Springer, vol. 59(1), pages 379-397, October.
    7. Woodside-Oriakhi, M. & Lucas, C. & Beasley, J.E., 2011. "Heuristic algorithms for the cardinality constrained efficient frontier," European Journal of Operational Research, Elsevier, vol. 213(3), pages 538-550, September.
    8. Tahereh Khodamoradi & Maziar Salahi & Ali Reza Najafi, 2021. "Cardinality-constrained portfolio optimization with short selling and risk-neutral interest rate," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 197-214, June.
    9. Belaïd Aouni & Cinzia Colapinto & Davide Torre, 2013. "A cardinality constrained stochastic goal programming model with satisfaction functions for venture capital investment decision making," Annals of Operations Research, Springer, vol. 205(1), pages 77-88, May.
    10. Mansini, Renata & Ogryczak, Wlodzimierz & Speranza, M. Grazia, 2014. "Twenty years of linear programming based portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 518-535.
    11. Zhou, Zhongbao & Jin, Qianying & Xiao, Helu & Wu, Qian & Liu, Wenbin, 2018. "Estimation of cardinality constrained portfolio efficiency via segmented DEA," Omega, Elsevier, vol. 76(C), pages 28-37.
    12. Wei Xu & Jie Tang & Ka Fai Cedric Yiu & Jian Wen Peng, 2024. "An Efficient Global Optimal Method for Cardinality Constrained Portfolio Optimization," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 690-704, March.
    13. Madani Bezoui & Mustapha Moulaï & Ahcène Bounceur & Reinhardt Euler, 2019. "An iterative method for solving a bi-objective constrained portfolio optimization problem," Computational Optimization and Applications, Springer, vol. 72(2), pages 479-498, March.
    14. Xiaojin Zheng & Xiaoling Sun & Duan Li, 2014. "Improving the Performance of MIQP Solvers for Quadratic Programs with Cardinality and Minimum Threshold Constraints: A Semidefinite Program Approach," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 690-703, November.
    15. Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2013. "A new method for mean-variance portfolio optimization with cardinality constraints," Annals of Operations Research, Springer, vol. 205(1), pages 213-234, May.
    16. Juan Francisco Monge, 2017. "Cardinality constrained portfolio selection via factor models," Papers 1708.02424, arXiv.org.
    17. K. Liagkouras & K. Metaxiotis, 2018. "A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem," Annals of Operations Research, Springer, vol. 267(1), pages 281-319, August.
    18. Jianjun Gao & Duan Li, 2013. "Optimal Cardinality Constrained Portfolio Selection," Operations Research, INFORMS, vol. 61(3), pages 745-761, June.
    19. Najafi, Alireza & Taleghani, Rahman, 2022. "Fractional Liu uncertain differential equation and its application to finance," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    20. Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2015. "Linear vs. quadratic portfolio selection models with hard real-world constraints," Computational Management Science, Springer, vol. 12(3), pages 345-370, July.

    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:56:y:2013:i:4:p:1441-1455. 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.