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Improved Accelerated Gradient Algorithms with Line Search for Smooth Convex Optimization Problems

Author

Listed:
  • Ting Li

    (School of Mathematical Sciences, Nanjing Normal University, Jiangsu Key Laboratory for NSLSCS, Nanjing 210023, P. R. China)

  • Yongzhong Song

    (School of Mathematical Sciences, Nanjing Normal University, Jiangsu Key Laboratory for NSLSCS, Nanjing 210023, P. R. China)

  • Xingju Cai

    (School of Mathematical Sciences, Nanjing Normal University, Jiangsu Key Laboratory for NSLSCS, Nanjing 210023, P. R. China)

Abstract

For smooth convex optimization problems, the optimal convergence rate of first-order algorithm is O(1/k2) in theory. This paper proposes three improved accelerated gradient algorithms with the gradient information at the latest point. For the step size, to avoid using the global Lipschitz constant and make the algorithm converge faster, new adaptive line search strategies are adopted. By constructing a descent Lyapunov function, we prove that the proposed algorithms can preserve the convergence rate of O(1/k2). Numerical experiments demonstrate that our algorithms perform better than some existing algorithms which have optimal convergence rate.

Suggested Citation

  • Ting Li & Yongzhong Song & Xingju Cai, 2024. "Improved Accelerated Gradient Algorithms with Line Search for Smooth Convex Optimization Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 41(03), pages 1-24, June.
    • Handle: RePEc:wsi:apjorx:v:41:y:2024:i:03:n:s0217595923500306
    DOI: 10.1142/S0217595923500306
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