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International Conference on Mechatronics and Intelligent Robotics

ICMIR 2017: Recent Developments in Mechatronics and Intelligent Robotics pp 229–233Cite as

A Discussion on the Application of the Smoothing Function of the Plus Function

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 691))

Abstract

In this paper, we analyze the smooth approximation property of a smoothing function of plus function. And these smooth approximation properties of the smoothing function can be applied to the complementarity problems, penalty functions, optimal control, and support vector machines. Thus, we can use smooth method to solve these problems, and these smooth approximation properties have a good effect in proving the convergence of the smooth method. Subsequently, the application of these good properties in solving practical problems is given.

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References

  1. Chen, X.J., Zhou, W.J.: Smoothing nonlinear conjugate gradient method for image restoration using nonsmooth nonconvex minimization. SIAM J. Imaging Sci. 3(4), 765–790 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  2. Chen, X.J.: Smoothing methods for nonsmooth, nonconvex minimization. Math. Progr. 134, 71–99 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chen, C., Mangasarian, O.L.: A class of smoothing functions for nonlinear and mixed complementarity problems. Comput. Optim. Appl. 5(2), 97–138 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. Lee, Y.J., Mangasarian, O.L.: A smooth support vector machine for classification. Comput. Optim. Appl. 20(1), 5–21 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Xiong, J.Z., Hu, J.L., Yuan, H.Q., Hu, T.M., Li, G.M.: Research on a new class of smoothing support vector machines. Acta Electr. Sin. 35(2), 366–370 (2007). (in Chinese)

    Google Scholar 

  6. Yuan, Y.B., Yan, J., Xu, C.X.: Polynomial smooth support vector machine. Chin. J. Comput. 28(1), 9–17 (2005). (in Chinese)

    Google Scholar 

  7. Zheng, J., Lu, B.L.: A support vector machine classifier with automatic confidence and its application to gender classification. Neurocomputing 74(11), 1926–1935 (2011)

    Article  Google Scholar 

  8. Zhou, X., Wang, Y., Wang, D.L.: Application of kernel methods in signals modulation classification. J. China Univ. Posts Telecommun. 18(1), 84–90 (2011)

    Article  Google Scholar 

  9. Zhao, Z.C.: Combining SVM and CHMM classifiers for porno video recognition. J. China Univ. Posts Telecommun. 19(3), 100–106 (2012)

    Article  Google Scholar 

  10. Lin, H.J., Yeh, J.P.: Optimal reduction of solutions for support vector machines. Appl. Math. Comput. 214(2), 329–335 (2009)

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematic and Statistics, Qingdao University, Qingdao, Shandong, 266071, China

    Shu-ting Shao & Shou-qiang Du

Authors
  1. Shu-ting Shao
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  2. Shou-qiang Du
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Corresponding author

Correspondence to Shu-ting Shao .

Editor information

Editors and Affiliations

  1. Shenyang Jianzhu University , Shenyang, China

    Feng Qiao

  2. SOA University , Bhubaneswar, India

    Srikanta Patnaik

  3. Montclair State University , Montclair, New Jersey, USA

    John Wang

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Cite this paper

Shao, St., Du, Sq. (2018). A Discussion on the Application of the Smoothing Function of the Plus Function. In: Qiao, F., Patnaik, S., Wang, J. (eds) Recent Developments in Mechatronics and Intelligent Robotics. ICMIR 2017. Advances in Intelligent Systems and Computing, vol 691. Springer, Cham. https://doi.org/10.1007/978-3-319-70990-1_34

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  • DOI: https://doi.org/10.1007/978-3-319-70990-1_34

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70989-5

  • Online ISBN: 978-3-319-70990-1

  • eBook Packages: EngineeringEngineering (R0)

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