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

Ting Li (), Yongzhong Song () and Xingju Cai
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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

Asia-Pacific Journal of Operational Research (APJOR), 2024, vol. 41, issue 03, 1-24

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.

Keywords: Adaptive step size; Nesterov acceleration algorithm; accelerated gradient algorithm; Lyapunov function; l2 regularized logistic regression (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0217595923500306

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