Virginia TechWang, ZhenboFang, Sue- CherngGao, David Y.Xing, Wenxun2014-05-142014-05-142008-05Wang, Z. B.; Fang, S. C.; Gao, D. Y.; Xing, W. X., "Global extremal conditions for multi-integer quadratic programming," J. Industrial and Management Optimization 4(2), 213-225, (2008); DOI: 10.3934/jimo.2008.4.2131547-5816http://hdl.handle.net/10919/47976Support vector machine (SVM) is a very popular method for binary data classification in data mining ( machine learning). Since the objective function of the unconstrained SVM model is a non-smooth function, a lot of good optimal algorithms can't be used to find the solution. In order to overcome this model's non-smooth property, Lee and Mangasarian proposed smooth support vector machine (SSVM) in 2001. Later, Yuan et al. proposed the polynomial smooth support vector machine (PSSVM) in 2005. In this paper, a three-order spline function is used to smooth the objective function and a three-order spline smooth support vector machine model (TSSVM) is obtained. By analyzing the performance of the smooth function, the smooth precision has been improved obviously. Moreover, BFGS and Newton-Armijo algorithms are used to solve the TSSVM model. Our experimental results prove that the TSSVM model has better classification performance than other competitive baselines.en-USIn Copyrightquadratic programmingdata miningsupport vector machineconstrained variational-inequalitiesunconstrained optimizationcomplementarity-problemsglobal optimizationperfect dualityengineering, multidisciplinaryoperations research & managementsciencemathematics, interdisciplinary applicationsArticle - Refereedhttp://www.aimsciences.org/journals/displayArticles.jsp?paperID=3258https://doi.org/10.3934/jimo.2008.4.213