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Two smooth support vector machines for $$\varepsilon $$ ε -insensitive regression

Author

Listed:
  • Weizhe Gu

    (Tianjin University)

  • Wei-Po Chen

    (National Taiwan Normal University)

  • Chun-Hsu Ko

    (I-Shou University)

  • Yuh-Jye Lee

    (National Chiao Tung University)

  • Jein-Shan Chen

    (National Taiwan Normal University)

Abstract

In this paper, we propose two new smooth support vector machines for $$\varepsilon $$ ε -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 $$\varepsilon $$ ε -support vector regression ( $$\varepsilon $$ ε -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.

Suggested Citation

  • Weizhe Gu & Wei-Po Chen & Chun-Hsu Ko & Yuh-Jye Lee & Jein-Shan Chen, 2018. "Two smooth support vector machines for $$\varepsilon $$ ε -insensitive regression," Computational Optimization and Applications, Springer, vol. 70(1), pages 171-199, May.
    • Handle: RePEc:spr:coopap:v:70:y:2018:i:1:d:10.1007_s10589-017-9975-9
    DOI: 10.1007/s10589-017-9975-9
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    References listed on IDEAS

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    1. Paul Tseng & Sangwoon Yun, 2010. "A coordinate gradient descent method for linearly constrained smooth optimization and support vector machines training," Computational Optimization and Applications, Springer, vol. 47(2), pages 179-206, October.
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    Cited by:

    1. Juan Yin & Qingna Li, 2019. "A semismooth Newton method for support vector classification and regression," Computational Optimization and Applications, Springer, vol. 73(2), pages 477-508, June.

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