  We investigate the problem of minimizing Kullback-Leibler divergence between
a linear model $Ax$ and a positive vector $b$ in different convex domains
(positive orthant, $n$-dimensional box, probability simplex). Our focus is on
the SMART method that employs efficient multiplicative updates. We explore the
exponentiated gradient method, which can be viewed as a Bregman proximal
gradient method and as a Riemannian gradient descent on the parameter manifold
of a corresponding distribution of the exponential family. This dual
interpretation enables us to establish connections and achieve accelerated
SMART iterates while smoothly incorporating constraints. The performance of the
proposed acceleration schemes is demonstrated by large-scale numerical
examples.
