Convergence results of a nested decentralized gradient method for non-strongly convex problems

We are concerned with the convergence of NEAR-DGD (Nested Exact Alternating Recursion Distributed Graident Descent) method introduced to solve the distributed optimization problems. Under the assumption of strong convexity and Lipschitz continuous gradient, the linear convergence is established in [1]. In this paper, we investigate the convergence property of NEAR-DGD in the absence of strong convexity. More precisely, we establish the convergence result in the case where only the convexity or the quasi-strong convexity is assumed on the objective function in place of the strong convexity. Numerical results are provided to support the convergence results.

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