On the primal-dual dynamics of Support Vector Machines
Provides a theoretical convergence guarantee for SVM optimization via dynamical systems, but is incremental as it applies existing passivity theory to a known problem.
This paper proves global asymptotic stability of a dynamical system formulation of SVM optimization using passivity theory, ensuring convergence to the optimal solution from any initial condition.
The aim of this paper is to study the convergence of the primal-dual dynamics pertaining to Support Vector Machines (SVM). The optimization routine, used for determining an SVM for classification, is first formulated as a dynamical system. The dynamical system is constructed such that its equilibrium point is the solution to the SVM optimization problem. It is then shown, using passivity theory, that the dynamical system is global asymptotically stable. In other words, the dynamical system converges onto the optimal solution asymptotically, irrespective of the initial condition. Simulations and computations are provided for corroboration.