Scholarlink

<p>In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full gradient computation are bottlenecks when dealing with large-scale problems. We propose a subspace quasi-Newton method that is restricted to a deterministic subspace together with a subspace gradient based on random matrix theory. Our method does not require full gradients, let alone Hessian matrices. Yet, it achieves the same order of worst-case iteration complexity in expectation for both convex and nonconvex cases as existing subspace methods. In numerical experiments, we confirm the superiority of our algorithm in terms of computation time.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Quasi-Newton method with subspace gradients

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月13日

查看全文
  • Taisei Miyaishi,
  • Ryota Nozawa,
  • Pierre-Louis Poirion,
  • Akiko Takeda

摘要

In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full gradient computation are bottlenecks when dealing with large-scale problems. We propose a subspace quasi-Newton method that is restricted to a deterministic subspace together with a subspace gradient based on random matrix theory. Our method does not require full gradients, let alone Hessian matrices. Yet, it achieves the same order of worst-case iteration complexity in expectation for both convex and nonconvex cases as existing subspace methods. In numerical experiments, we confirm the superiority of our algorithm in terms of computation time.