  We consider strongly convex distributed consensus optimization over connected
networks. EFIX, the proposed method, is derived using quadratic penalty
approach. In more detail, we use the standard reformulation { transforming the
original problem into a constrained problem in a higher dimensional space { to
define a sequence of suitable quadratic penalty subproblems with increasing
penalty parameters. For quadratic objectives, the corresponding sequence
consists of quadratic penalty subproblems. For the generic strongly convex
case, the objective function is approximated with a quadratic model and hence
the sequence of the resulting penalty subproblems is again quadratic. EFIX is
then derived by solving each of the quadratic penalty subproblems via a fixed
point (R)-linear solver, e.g., Jacobi Over-Relaxation method. The exact
convergence is proved as well as the worst case complexity of order
O(epsilon^-1) for the quadratic case. In the case of strongly convex generic
functions, a standard result for penalty methods is obtained. Numerical results
indicate that the method is highly competitive with state-of-the-art exact
first order methods, requires smaller computational and communication effort,
and is robust to the choice of algorithm parameters.
