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Distributed Convex Optimization on the Nonnegative Orthant

This paper considers distributed convex optimization problems with nonnegativity constraints on the decision variables. We propose a novel distributed gradient dynamics in continuous-time setting that can solve this problem. In contrast to the existing methods in the literature, we do not incorporate any Euclidean projection operators or penalty functions to obtain an approximate solution. We show that the proposed network flow is guaranteed to converge asymptotically, on any connected graph, to the unique global minimizer, provided that the aggregate objective function is strongly convex and the local cost functions have Lipschitz-continuous gradients.