Parallel decomposition methods for linearly constrained problems subject to simple bound with application to the SVMs training
We consider the convex quadratic linearly constrained problem
with bounded variables and with huge and dense Hessian matrix that arises
in many applications such as the training problem of bias support vector machines.
We propose a decomposition algorithmic scheme suitable to parallel implementations
and we prove global convergence under suitable conditions. Focusing
on support vector machines training, we outline how these assumptions
can be satisfied in practice and we suggest various specific implementations.
Extensions of the theoretical results to general linearly constrained problem
are provided. We included numerical results on support vector machines with
the aim of showing the viability and the effectiveness of the proposed scheme.