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Nonlinear optimization and support vector machines

Author

Listed:
  • Veronica Piccialli

    (Dipartimento di Ingegneria Informatica, Automatica e Gestionale “A. Ruberti”, Sapienza Università degli Studi di Roma)

  • Marco Sciandrone

    (Dipartimento di Ingegneria Informatica, Automatica e Gestionale “A. Ruberti”, Sapienza Università degli Studi di Roma)

Abstract

Support vector machine (SVM) is one of the most important class of machine learning models and algorithms, and has been successfully applied in various fields. Nonlinear optimization plays a crucial role in SVM methodology, both in defining the machine learning models and in designing convergent and efficient algorithms for large-scale training problems. In this paper we present the convex programming problems underlying SVM focusing on supervised binary classification. We analyze the most important and used optimization methods for SVM training problems, and we discuss how the properties of these problems can be incorporated in designing useful algorithms.

Suggested Citation

  • Veronica Piccialli & Marco Sciandrone, 2022. "Nonlinear optimization and support vector machines," Annals of Operations Research, Springer, vol. 314(1), pages 15-47, July.
    • Handle: RePEc:spr:annopr:v:314:y:2022:i:1:d:10.1007_s10479-022-04655-x
    DOI: 10.1007/s10479-022-04655-x
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    References listed on IDEAS

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    1. C. J. Lin & S. Lucidi & L. Palagi & A. Risi & M. Sciandrone, 2009. "Decomposition Algorithm Model for Singly Linearly-Constrained Problems Subject to Lower and Upper Bounds," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 107-126, April.
    2. Annabella Astorino & Antonio Fuduli, 2015. "Support Vector Machine Polyhedral Separability in Semisupervised Learning," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 1039-1050, March.
    3. E. Gertz & Joshua Griffin, 2010. "Using an iterative linear solver in an interior-point method for generating support vector machines," Computational Optimization and Applications, Springer, vol. 47(3), pages 431-453, November.
    4. Veronica Piccialli & Marco Sciandrone, 2018. "Nonlinear optimization and support vector machines," 4OR, Springer, vol. 16(2), pages 111-149, June.
    5. Cassioli, A. & Chiavaioli, A. & Manes, C. & Sciandrone, M., 2013. "An incremental least squares algorithm for large scale linear classification," European Journal of Operational Research, Elsevier, vol. 224(3), pages 560-565.
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