Global extremal conditions for multi-integer quadratic programming

Support 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.