  In this paper we consider a class of optimization problems with a strongly
convex objective function and the feasible set given by an intersection of a
simple convex set with a set given by a number of linear equality and
inequality constraints. A number of optimization problems in applications can
be stated in this form, examples being the entropy-linear programming, the
ridge regression, the elastic net, the regularized optimal transport, etc. We
extend the Fast Gradient Method applied to the dual problem in order to make it
primal-dual so that it allows not only to solve the dual problem, but also to
construct nearly optimal and nearly feasible solution of the primal problem. We
also prove a theorem about the convergence rate for the proposed algorithm in
terms of the objective function and the linear constraints infeasibility.
