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A Newton Tracking Algorithm with Exact Linear Convergence Rate for Decentralized Consensus Optimization

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Document pages: 9 pages

Abstract: This paper considers the decentralized consensus optimization problem definedover a network where each node holds a second-order differentiable localobjective function. Our goal is to minimize the summation of local objectivefunctions and find the exact optimal solution using only local computation andneighboring communication. We propose a novel Newton tracking algorithm, whereeach node updates its local variable along a local Newton direction modifiedwith neighboring and historical information. We investigate the connectionsbetween the proposed Newton tracking algorithm and several existing methods,including gradient tracking and second-order algorithms. Under the strongconvexity assumption, we prove that it converges to the exact optimal solutionat a linear rate. Numerical experiments demonstrate the efficacy of Newtontracking and validate the theoretical findings.

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