  We develop a methodology to automatically compute worst-case performance
bounds for a class of decentralized algorithms that optimize the average of
local functions distributed across a network. We extend the recently proposed
PEP approach to decentralized optimization. This approach allows computing the
exact worst-case performance and worst-case instance of centralized algorithms
by solving an SDP. We obtain an exact formulation when the network matrix is
given, and a relaxation when considering entire classes of network matrices
characterized by their spectral range. We apply our methodology to the
decentralized (sub)gradient method, obtain a nearly tight worst-case
performance bound that significantly improves over the literature, and gain
insights into the worst communication networks for a given spectral range.
