Support vector machine has become an increasingly popular tool for machine learning tasks involving classification, regression or novelty detection. Training a support vector machine requires the solution of a very large quadratic programming problem. Traditional optimization methods cannot be directly applied due to memory restrictions. Up to now, several approaches exist for circumventing the above shortcomings and work well. Another learning algorithm, particle swarm optimization, Quantum-behave Particle Swarm for training SVM is introduced. Another approach named least square support vector machine (LSSVM) and active set strategy are introduced. The obtained results by these methods are tested on a breast cancer dataset and compared with the exact solution model problem.