  The aim of this manuscript is to approach by means of first order
differential equations/inclusions convex programming problems with two-block
separable linear constraints and objectives, whereby (at least) one of the
components of the latter is assumed to be strongly convex. Each block of the
objective contains a further smooth convex function. We investigate the
dynamical system proposed and prove that its trajectories asymptotically
converge to a saddle point of the Lagrangian of the convex optimization
problem. Time discretization of the dynamical system leads to the alternating
minimization algorithm AMA and also to its proximal variant recently introduced
in the literature.
