  We develop a novel formulation of the Performance Estimation Problem (PEP)
for decentralized optimization whose size is independent of the number of
agents in the network. The PEP approach allows computing automatically the
worst-case performance and worst-case instance of first-order optimization
methods by solving an SDP. Unlike previous work, the size of our new PEP
formulation is independent of the network size. For this purpose, we take a
global view of the decentralized problem and we also decouple the consensus
subspace and its orthogonal complement. We apply our methodology to different
decentralized methods such as DGD, DIGing and EXTRA and obtain numerically
tight performance guarantees that are valid for any network size.
