Augmented lagrangian - Fast projected gradient algorithm with working set selection for training support vector machines

We present an algorithm for training Support Vector Machines (SVM) for classification based on fast projected gradient, augmented Lagrangian methods and a working set selection principle. The algorithm is capable of training SVM with tens of thousands data points within seconds on a modern personal computer system. The algorithm can be parallelized and therefore it is suitable for multi processor environment. We describe the algorithm, provide numerical results for solving medium size problems and discuss future directions of speeding up the SVM training. © 2021 Journal of Applied and Numerical Optimization.