Two smooth support vector machines for \(\varepsilon \)-insensitive regression

  • Weizhe Gu
  • Wei-Po Chen
  • Chun-Hsu Ko
  • Yuh-Jye Lee
  • Jein-Shan Chen


In this paper, we propose two new smooth support vector machines for \(\varepsilon \)-insensitive regression. According to these two smooth support vector machines, we construct two systems of smooth equations based on two novel families of smoothing functions, from which we seek the solution to \(\varepsilon \)-support vector regression (\(\varepsilon \)-SVR). More specifically, using the proposed smoothing functions, we employ the smoothing Newton method to solve the systems of smooth equations. The algorithm is shown to be globally and quadratically convergent without any additional conditions. Numerical comparisons among different values of parameter are also reported.


Support vector machine \(\varepsilon \)-insensitive loss \(\varepsilon \)-smooth support vector regression Smoothing Newton algorithm 


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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  • Weizhe Gu
    • 1
  • Wei-Po Chen
    • 2
  • Chun-Hsu Ko
    • 3
  • Yuh-Jye Lee
    • 4
  • Jein-Shan Chen
    • 2
  1. 1.Department of Mathematics, School of ScienceTianjin UniversityTianjinPeople’s Republic of China
  2. 2.Department of MathematicsNational Taiwan Normal UniversityTaipeiTaiwan
  3. 3.Department of Electrical EngineeringI-Shou UniversityKaohsiungTaiwan
  4. 4.Department of Applied MathematicsNational Chiao Tung UniversityHsinchuTaiwan

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