Abstract In this work we consider nonlinear minimization problems with a single linear equality constraint and box constraints. We are especially interested in solving problems where the number of variables is so large that traditional optimization methods cannot be directly applied. The Support Vector Machines (SVM) is a technique for machine learning problems. In this paper, we define a descent search direction selected among a suitable set of sparse feasible directions which have q (q>2, even) components to reduce the iteration numbers. Thus we put forward a new working set selection method for solving large scale support vector machines.