IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v503y2025ics0096300325002255.html

Min-min minimization for the fractional ℓ0-regularized problem

Author

Listed:
  • Wang, Jun
  • Ma, Qiang
  • Zhou, Cheng

Abstract

In this paper, we present a novel unconstrained fractional ℓ0 regularization (FL0R) model to solve cardinality minimization. Firstly, we construct an interesting min⁡−min minimization from FL0R by introducing a middle variable of sparsity. Then, we prove that the solution to min⁡−min minimization with a given sparsity is one of FL0R. Finally, some numerical examples are presented to illustrate the effectiveness and validity of the new model.

Suggested Citation

  • Wang, Jun & Ma, Qiang & Zhou, Cheng, 2025. "Min-min minimization for the fractional ℓ0-regularized problem," Applied Mathematics and Computation, Elsevier, vol. 503(C).
    • Handle: RePEc:eee:apmaco:v:503:y:2025:i:c:s0096300325002255
    DOI: 10.1016/j.amc.2025.129499
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300325002255
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2025.129499?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Christian Kanzow & Andreas B. Raharja & Alexandra Schwartz, 2021. "Sequential optimality conditions for cardinality-constrained optimization problems with applications," Computational Optimization and Applications, Springer, vol. 80(1), pages 185-211, September.
    2. Fan Wu & Wei Bian, 2020. "Accelerated iterative hard thresholding algorithm for $$l_0$$l0 regularized regression problem," Journal of Global Optimization, Springer, vol. 76(4), pages 819-840, April.
    3. Matteo Lapucci & Tommaso Levato & Marco Sciandrone, 2021. "Convergent Inexact Penalty Decomposition Methods for Cardinality-Constrained Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 473-496, February.
    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. Matteo Lapucci & Alessio Sortino, 2024. "On the Convergence of Inexact Alternate Minimization in Problems with $$\ell _0$$ ℓ 0 Penalties," SN Operations Research Forum, Springer, vol. 5(2), pages 1-11, June.
    2. Matteo Lapucci & Tommaso Levato & Francesco Rinaldi & Marco Sciandrone, 2023. "A Unifying Framework for Sparsity-Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 199(2), pages 663-692, November.
    3. N. Krejić & E. H. M. Krulikovski & M. Raydan, 2023. "A Low-Cost Alternating Projection Approach for a Continuous Formulation of Convex and Cardinality Constrained Optimization," SN Operations Research Forum, Springer, vol. 4(4), pages 1-24, December.
    4. Jean C. A. Medeiros & Ademir A. Ribeiro & Mael Sachine & Leonardo D. Secchin, 2025. "A Practical Second-Order Optimality Condition for Cardinality-Constrained Problems with Application to an Augmented Lagrangian Method," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-25, August.
    5. Renan W. Prado & Sandra A. Santos & Lucas E. A. Simões, 2023. "On the Fulfillment of the Complementary Approximate Karush–Kuhn–Tucker Conditions and Algorithmic Applications," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 705-736, May.
    6. Dongdong Zhang & Shaohua Pan & Shujun Bi & Defeng Sun, 2023. "Zero-norm regularized problems: equivalent surrogates, proximal MM method and statistical error bound," Computational Optimization and Applications, Springer, vol. 86(2), pages 627-667, November.
    7. Yan-Chao Liang & Gui-Hua Lin, 2024. "Relaxed method for optimization problems with cardinality constraints," Journal of Global Optimization, Springer, vol. 88(2), pages 359-375, February.
    8. R. Andreani & G. Haeser & A. Ramos & D. O. Santos & L. D. Secchin & A. Serranoni, 2025. "Strong global convergence properties of algorithms for nonlinear symmetric cone programming," Computational Optimization and Applications, Springer, vol. 91(2), pages 397-421, June.
    9. Christian Kanzow & Matteo Lapucci, 2023. "Inexact penalty decomposition methods for optimization problems with geometric constraints," Computational Optimization and Applications, Springer, vol. 85(3), pages 937-971, July.
    10. Didier Aussel & Daniel Lasluisa & David Salas, 2025. "Cardinality Constraints in Single-Leader-Multi-Follower Games," Journal of Optimization Theory and Applications, Springer, vol. 206(1), pages 1-27, July.
    11. Ademir A. Ribeiro & Mael Sachine & Evelin H. M. Krulikovski, 2022. "A Comparative Study of Sequential Optimality Conditions for Mathematical Programs with Cardinality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 1067-1083, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:apmaco:v:503:y:2025:i:c:s0096300325002255. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.