Abstract
This paper studies the convergence rate for distributed constrained optimization problems over unbalanced time-varying graphs, where the objective function is composed of an aggregate sum of local objective functions which are known to individual agents. In order to deal with the problem, a distributed proximal point algorithm (DPPA) is revisited, which does not necessitate the computation of subgradients, and the convergence is rigorously analyzed under mild assumptions with a class of general stepsizes, i.e., positive, decaying and non-summable. Besides, it is proved that the algorithm converges at the rate of $O(1 / \sqrt{k})$ in the ergodic sense with respect to the weight-averaged state of all agents, where k>0 is the iteration number. Moreover, the efficacy of the proposed algorithm is validated by a numerical example.
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