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This paper is concerned with a constrained optimization problem over adirected graph (digraph) of nodes, in which the cost function is a sum of localobjectives, and each node only knows its local objective and constraints. Tocollaboratively solve the optimization, most of the existing works require theinteraction graph to be balanced or "doubly-stochastic", which is quiterestrictive and not necessary as shown in this paper. We focus on an epigraphform of the original optimization to resolve the "unbalanced" problem, anddesign a novel two-step recursive algorithm with a simple structure. Understrongly connected digraphs, we prove that each node asymptotically convergesto some common optimal solution. Finally, simulations are performed toillustrate the effectiveness of the proposed algorithms.

Distributed Random-Fixed Projected Algorithm for Constrained Optimization Over Digraphs