IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v199y2023i3d10.1007_s10957-023-02317-x.html
   My bibliography  Save this article

Optimization of Sparsity-Constrained Neural Networks as a Mixed Integer Linear Program

Author

Listed:
  • Bodo Rosenhahn

    (Leibniz University)

Abstract

The literature has shown how to optimize and analyze the parameters of different types of neural networks using mixed integer linear programs (MILP). Building on these developments, this work presents an approach to do so for a McCulloch/Pitts and Rosenblatt neurons. As the original formulation involves a step-function, it is not differentiable, but it is possible to optimize the parameters of neurons, and their concatenation as a shallow neural network, by using a mixed integer linear program. The main contribution of this paper is to additionally enforce sparsity constraints on the weights and activations as well as on the amount of used neurons. Several experiments demonstrate that such constraints effectively prevent overfitting in neural networks, and ensure resource optimized models.

Suggested Citation

  • Bodo Rosenhahn, 2023. "Optimization of Sparsity-Constrained Neural Networks as a Mixed Integer Linear Program," Journal of Optimization Theory and Applications, Springer, vol. 199(3), pages 931-954, December.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:3:d:10.1007_s10957-023-02317-x
    DOI: 10.1007/s10957-023-02317-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-023-02317-x
    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/s10957-023-02317-x?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. David Bergman & Teng Huang & Philip Brooks & Andrea Lodi & Arvind U. Raghunathan, 2022. "JANOS: An Integrated Predictive and Prescriptive Modeling Framework," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 807-816, March.
    2. O. L. Mangasarian, 1993. "Mathematical Programming in Neural Networks," INFORMS Journal on Computing, INFORMS, vol. 5(4), pages 349-360, November.
    3. Gambella, Claudio & Ghaddar, Bissan & Naoum-Sawaya, Joe, 2021. "Optimization problems for machine learning: A survey," European Journal of Operational Research, Elsevier, vol. 290(3), pages 807-828.
    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. Eva K. Lee & Richard J. Gallagher & David A. Patterson, 2003. "A Linear Programming Approach to Discriminant Analysis with a Reserved-Judgment Region," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 23-41, February.
    2. M. V. Solodov, 1997. "Convergence Analysis of Perturbed Feasible Descent Methods," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 337-353, May.
    3. M. V. Solodov & S. K. Zavriev, 1998. "Error Stability Properties of Generalized Gradient-Type Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 663-680, September.
    4. Zhengyu Ma & Hong Seo Ryoo, 2021. "Spherical Classification of Data, a New Rule-Based Learning Method," Journal of Classification, Springer;The Classification Society, vol. 38(1), pages 44-71, April.
    5. H. D. Qi, 1999. "On Minimizing and Stationary Sequences of a New Class of Merit Functions for Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 411-431, August.
    6. W. Nick Street, 2005. "Oblique Multicategory Decision Trees Using Nonlinear Programming," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 25-31, February.
    7. Giovanni Felici & Klaus Truemper, 2002. "A MINSAT Approach for Learning in Logic Domains," INFORMS Journal on Computing, INFORMS, vol. 14(1), pages 20-36, February.
    8. P. S. Bradley & Usama M. Fayyad & O. L. Mangasarian, 1999. "Mathematical Programming for Data Mining: Formulations and Challenges," INFORMS Journal on Computing, INFORMS, vol. 11(3), pages 217-238, August.
    9. Andreas Dellnitz & Andreas Kleine & Madjid Tavana, 2024. "An integrated data envelopment analysis and regression tree method for new product price estimation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(4), pages 1189-1211, December.
    10. Palocsay, Susan W. & Stevens, Scott P. & Brookshire, Robert G. & Sacco, William J. & Copes, Wayne S. & Buckman, Robert F. & Smith, J. Stanley, 1996. "Using neural networks for trauma outcome evaluation," European Journal of Operational Research, Elsevier, vol. 93(2), pages 369-386, September.
    11. Keliang Wang & Leonardo Lozano & Carlos Cardonha & David Bergman, 2023. "Optimizing over an Ensemble of Trained Neural Networks," INFORMS Journal on Computing, INFORMS, vol. 35(3), pages 652-674, May.
    12. Doumpos, Michalis & Zopounidis, Constantin & Gounopoulos, Dimitrios & Platanakis, Emmanouil & Zhang, Wenke, 2023. "Operational research and artificial intelligence methods in banking," European Journal of Operational Research, Elsevier, vol. 306(1), pages 1-16.
    13. Sexton, Randall S. & Dorsey, Robert E. & Johnson, John D., 1999. "Optimization of neural networks: A comparative analysis of the genetic algorithm and simulated annealing," European Journal of Operational Research, Elsevier, vol. 114(3), pages 589-601, May.
    14. Miguel Angel Ortíz-Barrios & Dayana Milena Coba-Blanco & Juan-José Alfaro-Saíz & Daniela Stand-González, 2021. "Process Improvement Approaches for Increasing the Response of Emergency Departments against the COVID-19 Pandemic: A Systematic Review," IJERPH, MDPI, vol. 18(16), pages 1-31, August.
    15. Ítalo Santana & Breno Serrano & Maximilian Schiffer & Thibaut Vidal, 2025. "Support vector machines with the hard-margin loss: optimal training via combinatorial Benders’ cuts," Journal of Global Optimization, Springer, vol. 92(1), pages 205-225, May.
    16. Sobrie, Léon & Verschelde, Marijn & Roets, Bart, 2024. "Explainable real-time predictive analytics on employee workload in digital railway control rooms," European Journal of Operational Research, Elsevier, vol. 317(2), pages 437-448.
    17. Astorino, Annabella & Avolio, Matteo & Fuduli, Antonio, 2022. "A maximum-margin multisphere approach for binary Multiple Instance Learning," European Journal of Operational Research, Elsevier, vol. 299(2), pages 642-652.
    18. Chenbo Shi & Mohsen Emadikhiav & Leonardo Lozano & David Bergman, 2024. "Constraint Learning to Define Trust Regions in Optimization over Pre-Trained Predictive Models," INFORMS Journal on Computing, INFORMS, vol. 36(6), pages 1382-1399, December.
    19. Orsenigo, Carlotta & Vercellis, Carlo, 2004. "Discrete support vector decision trees via tabu search," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 311-322, September.
    20. Alcántara Mata, Antonio & Ruiz Mora, Carlos & Tsay, Calvin, 2024. "A Quantile Neural Network Framework for Twostage Stochastic Optimization," DES - Working Papers. Statistics and Econometrics. WS 43773, Universidad Carlos III de Madrid. Departamento de Estadística.

    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:spr:joptap:v:199:y:2023:i:3:d:10.1007_s10957-023-02317-x. 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.