Support Vector Machines in the primal

Support Vector Machines in the primal

Good news: you don't need to know anything about Lagrange multipliers, KKT conditions and duality to train an SVM. Have a look at

O. Chapelle, Training a Support Vector Machine in the Primal, Neural Computation, in press.
Matlab code (with an example). It should be faster than standard SVM solvers in the linear case (the complexity is linear in the number of training examples) and comparable in the nonlinear case (but it requires the whole kernel matrix to fit in memory).
For a C++ implementation of a primal linear SVM, you can use the SVMlin package (designed more generally for semi-supervised learning).

For large scale problems, a reduced set expansion can be used:

S. S. Keerthi, O. Chapelle, D. DeCoste, Building Support Vector Machines with Reduced Classifier Complexity, JMLR 7, 2006.
Matlab code and example (requires the kernel function).

Send me an email if you have any question.