In this article, we propose a novel dual inexact splitting algorithm (DISA) for distributed convex compositeoptimization problems, where the local loss function consists of a smooth term and a possibly nonsmooth term...
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In this article, we propose a novel dual inexact splitting algorithm (DISA) for distributed convex compositeoptimization problems, where the local loss function consists of a smooth term and a possibly nonsmooth term composed of a linear mapping. The DISA, for the first time, eliminates the dependence of the convergent step-size range on the Euclidean norm of the linear mapping, while inheriting the advantages of the classic primal-dual proximal splitting algorithm (PD-PSA): simple structure and easy implementation. This indicates that the DISA can be executed without prior knowledge of the norm, and tiny step sizes can be avoided when the norm is large. In addition, we prove sublinear and linear convergence rates of DISA under general convexity and metric subregularity, respectively. Moreover, we provide a variant of DISA with approximate proximal mapping and prove its global convergence and sublinear convergence rate. Numerical experiments corroborate our theoretical analyses and demonstrate a significant acceleration of the DISA compared to the existing PD-PSAs
In this article, we address a compositeoptimization problem in a distributed network. Each agent in the network possesses a private local convex function consisting of a differentiable term, a nonsmooth term, and a n...
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In this article, we address a compositeoptimization problem in a distributed network. Each agent in the network possesses a private local convex function consisting of a differentiable term, a nonsmooth term, and a nonsmooth term combined with a linear operator. The objective is to minimize the sum of all local functions while achieving consensus among the local states through information exchange with neighboring agents. To tackle this problem, we propose a novel distributed proximal alternating direction multiplier method (ADMM). By introducing the proximal operator of the nonsmooth term, linearizing the smooth term, and incorporating an additional proximal term, the ADMM subproblem can be solved more efficiently. One key advantage of the proposed algorithm is that it allows each agent to select parameters without being constrained by the network topology. In some instances, the algorithm can be transformed into some classical optimization algorithms. The algorithm is further extended to an asynchronous version by introducing randomized block coordinate. We further analyze the convergence of the proposed asynchronous algorithm and establish the sublinear convergence rate under synchronous conditions. Finally, several numerical experiments are conducted to verify the effectiveness of the proposed algorithm.
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