A smoothing multiple support vector machine model

Abstract

In this paper, we study a smoothing multiple support vector machine (SVM) by using exact penalty function. First, we formulate the optimization problem of multiple SVM as an unconstrained and nonsmooth optimization problem via exact penalty function. Then, we propose a two-order differentiable function to approximately smooth the exact penalty function, and get an unconstrained and smooth optimization problem. By error analysis, we can get approximate solution of multiple SVM by solving its approximately smooth penalty optimization problem without constraint. Finally, we give a corporate culture model by using multiple SVM as a factual example. Compared with artificial neural network, the precision of our smoothing multiple SVM which is illustrated with the numerical experiment is better. © Springer-Verlag Berlin Heidelberg 2006.