  A two-user downlink network aided by a reconfigurable intelligent surface is
considered. The weighted sum signal to interference plus noise ratio
maximization and the sum rate maximization models are presented, where the
precoding vectors and the RIS matrix are jointly optimized. Since the
optimization problem is non-convex and difficult, new approximation models are
proposed. The upper bounds of the corresponding objective functions are derived
and maximized. Two new algorithms based on the alternating direction method of
multiplier are proposed. It is proved that the proposed algorithms converge to
the KKT points of the approximation models as long as the iteration points
converge. Simulation results show the good performances of the proposed models
compared to state of the art algorithms.
