The decomposition method is generally used to
solve the quadratic program of Support Vector Machines.
The rate of convergence of this method is largely dependant on the sequence of sub-problems solved. In order to
study ways of increasing the convergence, we propose a
dynamic system perspective to model the dynamics of the
decomposition method. In particular, the minimization of a
sub-problem can be viewed as an autonomous dissipative
system in terms of second order differential equations. The
gradients of the sub-problems and the inequality constraints
are explicitly modelled as system variables. Using these
models, we then define a general decomposition method
as a non-autonomous system composed of sub-systems that
operate for discrete time intervals. The dependance of this
system on time is depicted by a time dependant permutation
matrix which functions as an indicator for operating subsystem components.