An Extended Gradient Method for Smooth and Strongly Convex Functions

Xuexue Zhang, Sanyang Liu () and Nannan Zhao ()
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Xuexue Zhang: School of Mathematics and Statistics, Xidian University, Xi’an 710126, China
Sanyang Liu: School of Mathematics and Statistics, Xidian University, Xi’an 710126, China
Nannan Zhao: School of Science, Chang’an University, Xi’an 710064, China

Mathematics, 2023, vol. 11, issue 23, 1-14

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.

Keywords: gradient method; decentralized optimization; strongly convex optimization; acceleration; convergence analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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