Abstract
We consider a distributed constrained optimization problem over graphs, where cost function of each agent is private. Moreover, we assume that the graphs are time-varying and directed. In order to address such problem, a fully decentralized stochastic subgradient projection algorithm is proposed over time-varying directed graphs. However, since the graphs are directed, the weight matrix may not be a doubly stochastic matrix. Therefore, we overcome this difficulty by using weight-balancing technique. By choosing appropriate step-sizes, we show that iterations of all agents asymptotically converge to some optimal solutions. Further, by our analysis, convergence rate of our proposed algorithm is O(ln Γ/Γ) under local strong convexity, where Γ is the number of iterations. In addition, under local convexity, we prove that our proposed algorithm can converge with rate O(ln Γ/Γ). In addition, we verify the theoretical results through simulations.
Highlights
We focus on distributed constrained optimization problems, which have arisen in many applications
We first present an asymptotic convergence of the distributed stochastic subgradient projection algorithms (4)-(5) with appropriately chosen step-sizes
We have proposed a fully decentralized stochastic subgradient projection algorithm to solve distributed constrained optimization problem over time-varying directed networks
Summary
We focus on distributed constrained optimization problems, which have arisen in many applications. Assume that each local cost function is strongly convex; even if all agents have access to their own noisy subgradient, our proposed algorithm is asymptotically convergent with rate O(ln Γ/Γ). Our goal is to design a distributed optimization algorithm and analyze the properties of the proposed algorithm, based on weight-balancing over time-varying directed networks. (i) We propose a distributed stochastic subgradient projection algorithm based on weight-balancing over time-varying directed networks. As with [24], every agent i updates its weight wi(τ) over time-varying directed networks as follows: wi A distributed stochastic subgradient projection algorithm is proposed to solve constrained optimization problem (1) over time-varying directed networks. The main results of the paper are presented
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