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An Extended Gradient Method for Smooth and Strongly Convex Functions

Author

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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)

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.

Suggested Citation

  • Xuexue Zhang & Sanyang Liu & Nannan Zhao, 2023. "An Extended Gradient Method for Smooth and Strongly Convex Functions," Mathematics, MDPI, vol. 11(23), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4771-:d:1288013
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    References listed on IDEAS

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    1. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2011. "First-order methods of smooth convex optimization with inexact oracle," LIDAM Discussion Papers CORE 2011002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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