AI 中文总结
本文提出一种基于Moreau-Yosida正则化的Wolfe型谱共轭梯度方法，证明其全局与R-线性收敛性，在基准及大规模非光滑凸优化问题上表现优于或匹配现有方法。
AI 中文摘要
本文针对非光滑凸优化问题，提出一种Wolfe型谱共轭梯度方法，该方法基于目标函数的Moreau-Yosida正则化构建。该方法结合了带保护措施的谱参数与Dai-Kou型共轭参数，并采用与正则化产生的不精确梯度兼容的Wolfe型线搜索。我们证明了该方法的全局收敛性，以及在额外强凸性假设下的R-线性收敛速率。将该方法在标准非光滑优化基准及大规模问题上进行评估，并与多种现有共轭梯度及束型方法对比。结果表明，所提方法整体表现具有竞争力，在多数测试问题上与现有方法相当或更优，同时也指出并讨论了当前实现的若干特定局限。
英文摘要
This paper proposes a Wolfe-type spectral conjugate gradient method for nonsmooth convex optimization, built on the Moreau-Yosida regularization of the objective function. The method combines a safeguarded spectral parameter with a Dai-Kou-type conjugate parameter, and uses a Wolfe-type line search compatible with the inexact gradients that the regularization produces. We establish global convergence of the method, together with an R-linear convergence rate under an additional strong-convexity assumption. The method is evaluated on standard nonsmooth optimization benchmarks and on large-scale problems, and compared against several existing conjugate gradient and bundle-type methods. The results show that the proposed method performs competitively overall, matching or outperforming existing methods on most problems tested, while a few specific limitations of the current implementation are also identified and discussed
Comments15 pages
