  Modern power systems are now in continuous process of massive changes.
Increased penetration of distributed generation, usage of energy storage and
controllable demand require introduction of a new control paradigm that does
not rely on massive information exchange required by centralized approaches.
Distributed algorithms can rely only on limited information from neighbours to
obtain an optimal solution for various optimization problems, such as optimal
power flow, unit commitment etc.
  As a generalization of these problems we consider the problem of
decentralized minimization of the smooth and convex partially separable
function $f = \sum_{k=1}^l f^k(x^k,\tilde x)$ under the coupled $\sum_{k=1}^l
(A^k x^k - b^k) \leq 0$ and the shared $\tilde{A} \tilde{x} - \tilde{b} \leq 0$
affine constraints, where the information about $A^k$ and $b^k$ is only
available for the $k$-th node of the computational network.
  One way to handle the coupled constraints in a distributed manner is to
rewrite them in a distributed-friendly form using the Laplace matrix of the
communication graph and auxiliary variables (Khamisov, CDC, 2017). Instead of
using this method we reformulate the constrained optimization problem as a
saddle point problem (SPP) and utilize the consensus constraint technique to
make it distributed-friendly. Then we provide a complexity analysis for
state-of-the-art SPP solving algorithms applied to this SPP.
