  In this paper, a primal-dual gradient flow algorithm for distributed support
vector machines (DSVM) is proposed. A network of computing nodes, each carrying
a subset of horizontally partitioned large dataset is considered. The nodes are
represented as dynamical systems with Arrow-Hurwicz-Uzawa gradient flow
dynamics, derived from the Lagrangian function of the DSVM problem. It is first
proved that the nodes are passive dynamical systems. Then, by employing the
Krasovskii type candidate Lyapunov functions, it is proved that the computing
nodes asymptotically converge to the optimal primal-dual solution.

Optimization and Control