  We propose a projected semi-stochastic gradient descent method with
mini-batch for improving both the theoretical complexity and practical
performance of the general stochastic gradient descent method (SGD). We are
able to prove linear convergence under weak strong convexity assumption. This
requires no strong convexity assumption for minimizing the sum of smooth convex
functions subject to a compact polyhedral set, which remains popular across
machine learning community. Our PS2GD preserves the low-cost per iteration and
high optimization accuracy via stochastic gradient variance-reduced technique,
and admits a simple parallel implementation with mini-batches. Moreover, PS2GD
is also applicable to dual problem of SVM with hinge loss.
