Convergence of the extended Lagrangian support vector machine

The Lagrangian support vector machine (LSVM) cannot solve large problems for nonlinear kernel classifiers. In order to extend the LSVM to solve very large problems, an extended Lagrangian support vector machine (ELSVM) for classifications based on LSVM and SVM^light has been presented by the authors. The idea of this paper for the ELSVM is to divide a large quadratic programming problem into a series of sub-problems with small size and to solve them via the LSVM. Since the LSVM can solve small and medium problems very fast for nonlinear kernel classifiers, the ELSVM can be used to handle large problems very efficiently. Numerical experiments on different types of problems have been conducted to demonstrate the high efficiency of the ELSVM. In this paper, the convergence for the ELSVM is proved theoretically to firmly establish the algorithm.