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

  • Shu-ting ShaoEmail author
  • Shou-qiang Du
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 691)


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.


Plus function Smoothing function Gradient consistency 


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.School of Mathematic and StatisticsQingdao UniversityQingdaoChina

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