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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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)
Chen, X.J.: Smoothing methods for nonsmooth, nonconvex minimization. Math. Progr. 134, 71–99 (2012)
Chen, C., Mangasarian, O.L.: A class of smoothing functions for nonlinear and mixed complementarity problems. Comput. Optim. Appl. 5(2), 97–138 (1996)
Lee, Y.J., Mangasarian, O.L.: A smooth support vector machine for classification. Comput. Optim. Appl. 20(1), 5–21 (2001)
**ong, 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)
Yuan, Y.B., Yan, J., Xu, C.X.: Polynomial smooth support vector machine. Chin. J. Comput. 28(1), 9–17 (2005). (in Chinese)
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)
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)
Zhao, Z.C.: Combining SVM and CHMM classifiers for porno video recognition. J. China Univ. Posts Telecommun. 19(3), 100–106 (2012)
Lin, H.J., Yeh, J.P.: Optimal reduction of solutions for support vector machines. Appl. Math. Comput. 214(2), 329–335 (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-70990-1_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-70989-5
Online ISBN: 978-3-319-70990-1
eBook Packages: EngineeringEngineering (R0)