关键词: 支持向量机, 广义支持向量机, 模式识别, 分类, 光滑函数, 多项式

Abstract: To solve the optimization problem of Generalized Support Vector Machine（GSVM），the primal optimization problem with inequality constraints is transformed into the unconstraint optimization problem，whose objective function is nonsmooth，therefore a series of polynomial smooth functions is introduced to approach the objective function.Different polynomial functions can be used according to the corresponding accuracy demand.The model is solved by the BFGS algorithm.Experimental results show，compared with the existing algorithms used for solving the optimization problem of GSVM，the proposed algorithm achieves higher testing accuracy more quickly and is useful for large-scale data.Therefore，the proposed algorithm is effective.

Key words: Support Vector Machine（SVM）, generalized support vector machines, pattern recognition, classification, smooth function, polynomial