An Accelerated Regularized Chebyshev–Halley Method for Unconstrained Optimization

Jianyu Xiao (), Haibin Zhang () and Huan Gao
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Jianyu Xiao: Beijing Institute for Scientific and Engineering Computing, Faculty of Science, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, P. R. China
Haibin Zhang: Beijing Institute for Scientific and Engineering Computing, Faculty of Science, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, P. R. China
Huan Gao: College of Mathematics and Computational Science, Hunan First Normal University, 1015 Fenglin 3rd Road, Yuelu District, Changsha, Hunan 410205, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2023, vol. 40, issue 04, 1-11

Abstract: In machine learning, most models can be transformed into unconstrained optimization problems, so how to solve the unconstrained optimization problem for different objective functions is always a hot issue. In this paper, a class of unconstrained optimization where objection function has pth-order derivative and Lipschitz continuous simultaneously is studied. To handle such problems, we propose an accelerated regularized Chebyshev–Halley method based on the Accelerated Hybrid Proximal Extragradient (A-HPE) framework. It proves that convergence complexity of the proposed method is O(𠜀−1 5), which is consistent with the lower iteration complexity bound for third-order tensor methods. Numerical experiments on functions in machine learning demonstrate the promising performance of the proposed method.

Keywords: Unconstrained optimization; convergence complexity; tensor methods; machine learning (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0217595923400080

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