Abstract
In this work, we introduce an extended gradient method that employs the gradients of the preceding two iterates to construct the search direction for the purpose of solving the centralized and decentralized smooth and strongly convex functions. Additionally, we establish the linear convergence for iterate sequences in both the centralized and decentralized manners. Furthermore, the numerical experiments demonstrate that the centralized extended gradient method can achieve faster acceleration than the compared algorithms, and the search direction also exhibits the capability to improve the convergence of the existing algorithms in both two manners.
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