A Smoothing Support Vector Machine Based on Quarter Penalty Function

Abstract

It is very important to find out a smoothing support vec- tor machine. This paper studies a smoothing support vec- tor machine (SVM) by using quarter penalty function. We introduce the optimization problem of SVM with an uncon- strained and nonsmooth optimization problem via quarter penalty function. Then, we define a one-order differentiable function to approximately smooth the penalty function, and get an unconstrained and smooth optimization problem. By error analysis, we may obtain approximate solution of SVM by solving its approximately smooth penalty optimization problem without constraints. The numerical experiment shows that our smoothing SVM is efficient.