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<p>Inertial extrapolation, as an acceleration method, has become increasingly popular in large-scale unconstrained optimization in recent years, due to its characteristic of effectively using historical iterative information to predict the next iteration point. The majority of these problems are smooth, and extensive research on nonsmooth problems is lacking. A novel iteration scheme, which integrates inertial extrapolation, is introduced in this paper. Drawing from the scheme, we propose an inertial Hestenes and Stiefel type (IHST) conjugate gradient method designed for addressing large-scale nonsmooth optimization problems. The method ensures sufficient descent property, exhibits trust-region feature, and demonstrates global convergence under suitable conditions. Numerical experiments confirm the exceptional effectiveness of the method in tackling large-scale nonsmooth optimization problems, solving both convex as well as non-convex problems across dimensions up to 100,000. Furthermore, we propose two extensions of the IHST method to enhance its applicability, exhibiting strong competitiveness in image restoration and machine learning applications.</p>

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An inertial Hestenes-Stiefel algorithm for nonsmooth convex optimization and its applications in machine learning

  • 期刊论文

  • 发表日期：

    2025年3月10日

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  • Jiahuan Tang,
  • Chen Ouyang,
  • Hongtruong Pham,
  • Gonglin Yuan

摘要

Inertial extrapolation, as an acceleration method, has become increasingly popular in large-scale unconstrained optimization in recent years, due to its characteristic of effectively using historical iterative information to predict the next iteration point. The majority of these problems are smooth, and extensive research on nonsmooth problems is lacking. A novel iteration scheme, which integrates inertial extrapolation, is introduced in this paper. Drawing from the scheme, we propose an inertial Hestenes and Stiefel type (IHST) conjugate gradient method designed for addressing large-scale nonsmooth optimization problems. The method ensures sufficient descent property, exhibits trust-region feature, and demonstrates global convergence under suitable conditions. Numerical experiments confirm the exceptional effectiveness of the method in tackling large-scale nonsmooth optimization problems, solving both convex as well as non-convex problems across dimensions up to 100,000. Furthermore, we propose two extensions of the IHST method to enhance its applicability, exhibiting strong competitiveness in image restoration and machine learning applications.