Abstract: A complementarity support vector machine was obtained which is based on a ammended problem of surpport vector machine. By using Fischer-Burmeister function,a new descent algorithm for support vector machine optimization problem was presented. The proposed algorithm does not base on the primal quadratic programming problem of SVM,but a complementarity problem. It mustn't compute any Hesse or the inverse matrix with simple and small computational work. And the shortcoming of Lagrangian method proposed by Mangasarian et al.,which need compute the inverse matrix that is not adapted to handle nonlinear largcscale classification problems, is overcomed. Furthermore, without any assumption, the global convegence is proved. Numerical experiments show that the algorithm is feasible and effective.

Key words: Support vector machines, Complementarity problem, Descent method, Global convergence