Stability analysis of the decomposition method for solving support vector machines

Abstract

situations where processing memory is limited, the Support Vector Machine quadratic program can be decomposed into smaller sub-problems and solved sequentially. The convergence of this method has been proven previously through the use of a counting method. In this initial investigation, we approach the convergence analysis by treating the decomposed sub-problems as subsystems of a general system. The gradients of the subprobkms and the inequality-constraints are explicitly modelled as system variables. The change in these variables during optimization form a dynamic system modelled by vector differential equations. We show that the change in the objective function can be written as the energ..