This paper considers a distributed convex optimization problem withinequality constraints over time-varying unbalanced digraphs, where the costfunction is a sum of local objectives, and each node of the graph only knowsits local objective and inequality constraints. Although there is a vastliterature on distributed optimization, most of them require the graph to bebalanced, which is quite restrictive and not necessary. Very recently, theunbalanced problem has been resolved only for either time-invariant graphs orunconstrained optimization. This work addresses the unbalancedness by focusingon an epigraph form of the constrained optimization. A striking feature is thatthis novel idea can be easily used to study time-varying unbalanced digraphs.Under local communications, a simple iterative algorithm is then designed foreach node. We prove that if the graph is uniformly jointly strongly connected,each node asymptotically converges to some common optimal solution.
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