Research On Support Vector Machine Algorithm Based On Variational Inequalities

Support vector machine algorithm is one of the hottest research in machine learn-ing. It has unique advantages in dealing with data classification problems, and can be widely applied to other machine learning problems. The traditional support vector ma-chine algorithms sometime spend too long training time or too much computation in dealing with large-scale data classification, which makes them need to be optimized.In this thesis, we transform the convex optimization problem in support vector machine into the equivalent variational inequality problem, and construct four new iterative algorithms to solve the equivalent variational inequalities, which are based on the idea of Customized proximal point algorithm, Alternating direction method of multipliers, Inertial proximal point algorithm and Inertial proximal point algorithm with alternating inertial steps. We prove that all of the four algorithms can converge to a solution of the variaitonal inequailtiy problem, and have a stable convergence rate of o(1/k). Finally, we use some data sets of UCI to do numerical experiment on these four new algorithms, and use the Sequential minimal optimization algorithm as a comparison algorithm. We testify that the four improved algorithms have better practical results.