A modified algorithm for Lagrangian multi-class support vector machine

This paper establishes finite termination of Newton method for minimizing a strongly convex, piecewise quadratic function on the n -dimensional real space _R². We start with a new formulation which is proposed based on the K-SVCR method. Then transform it as a complementarity problem and further a strongly convex unconstrained optimization problem by using the implicit Lagrangian function. A fast Newton algorithm with global and finite termination properties is established for solving the resulting optimization problem. Preliminary numerical experiments on benchmark datasets show that the algorithm has good performance on both accuracy and training speed.