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<p>The memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is an efficient approach for solving large-scale optimization problems. In this study, we propose a memoryless BFGS projection method for large-scale convexly constrained monotone equations. Specifically, we develop an improved memoryless BFGS search direction by incorporating a novel truncation scheme and a restart procedure, and design a new self-adjusting line search criterion. The search direction generated by the proposed method satisfies the sufficient descent condition, without relying on any additional assumptions. Moreover, its convergence can be proven without the Lipschitz continuity of the objective mapping, while the iteration complexity is proven under the local Lipschitz continuity. Finally, numerical experiments validate the effectiveness of the presented method; furthermore, its linear convergence rate is verified by a group experiments.</p>

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A memoryless Broyden-Fletcher-Goldfarb-Shanno-type projection method with self-adjusting line search for convexly constrained monotone equations and its applications

  • 期刊论文

  • 发表日期：

    2026年2月28日

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  • Xianzhen Jiang,
  • Yuchen Deng,
  • Jinbao Jian

摘要

The memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is an efficient approach for solving large-scale optimization problems. In this study, we propose a memoryless BFGS projection method for large-scale convexly constrained monotone equations. Specifically, we develop an improved memoryless BFGS search direction by incorporating a novel truncation scheme and a restart procedure, and design a new self-adjusting line search criterion. The search direction generated by the proposed method satisfies the sufficient descent condition, without relying on any additional assumptions. Moreover, its convergence can be proven without the Lipschitz continuity of the objective mapping, while the iteration complexity is proven under the local Lipschitz continuity. Finally, numerical experiments validate the effectiveness of the presented method; furthermore, its linear convergence rate is verified by a group experiments.