Methods and apparatus for building a support vector machine classifier

Solving a quadratic programming problem involved in training support vector machines by sweeping through a set of training examples, solving small sub-problems of the quadratic programming problem. Each of these sub-problems has an analytic solution, which is faster that the numerical quadratic programming solutions used in the prior art. In one embodiment, training examples with non-optimal Lagrange multipliers are adjusted, one at a time, until all are optimal (e.g. until all examples fulfill the Kuhn-Tucker conditions). In another embodiment, training examples with non-optimal Lagrange multipliers are paired and then adjusted, until all are optimal.