A general convergence theorem for the decomposition method

Abstract

The decomposition method is currently one of the major methods for solving the convex quadratic optimization problems being associated with support vector machines. Although there exist some versions of the method that are known to converge to an optimal solution, the general convergence properties of the method are not yet fully understood. In this paper, we present a variant of the decomposition method that basically converges for any convex quadratic optimization problem provided that the policy for working set selection satisfies three abstract conditions. We furthermore design a concrete policy that meets these requirements.