A smoothing support vector machine based on exact penalty function

In this paper, we study a smoothing support vector machine (SVM) by using exact penalty function. First, we formulate the optimization problem of SVM as an unconstrained and nonsmooth optimization problem via exact penalty function. Second, we propose a two-order differentiable function to approximately smooth the exact penalty function, and get an unconstrained and smooth optimization problem. Third, by error analysis, we can get approximate solution of SVM by solving its approximately smooth penalty optimization problem without constraint. Compared with artificial neural network and time sequence, the precision of prediction of our smoothing SVM which is illustrated with the numerical experiment is better.