  In this paper, we consider an unconstrained distributed optimization problem
over a network of agents, in which some agents are adversarial. We solve the
problem via gradient-based distributed optimization algorithm and characterize
the effect of the adversarial agents on the convergence of the algorithm to the
optimal solution. The attack model considered is such that agents locally
perturb their iterates before broadcasting it to neighbors; and we analyze the
case in which the adversarial agents cooperate in perturbing their estimates
and the case where each adversarial agent acts independently. Based on the
attack model adopted in the paper, we show that the solution converges to the
neighborhood of the optimal solution and depends on the magnitude of the attack
(perturbation) term. The analyses presented establishes conditions under which
the malicious agents have enough information to obstruct convergence to the
optimal solution by the non-adversarial agents.
