Decomposition for structured convex programs with smooth multiplier methods

We combine here these two ideas to develop decomposition schemes for solving structured convex programs with smooth Lagrangians, allowing the use of Newton types methods. We will concentrate our numerical analysis on an exponential and modified logarithmic barrier type of augmented Lagrangians leading to an alternating direction type algorithm. Numerical examples illustrating the performance of this algorithm versus classical quadratic alternating direction methods will be presented.