发表机构
University of Delhi; Indian Institute of Technology Roorkee; University of Duisburg-Essen（德里大学; 罗尔基印度理工学院; 杜伊斯堡-埃森大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对广义DC规划问题，提出两种惯性参数化Douglas-Rachford型算法，经实验验证其在稀疏恢复、鲁棒分类任务中性能优于现有同类算法。
AI 中文摘要
我们提出两种新型Douglas-Rachford型算法，用于求解广义DC规划问题。具体而言，在希尔伯特空间框架下，我们处理两个可能非光滑凸函数之和的最小化问题，其中减去一个具有Lipschitz连续梯度的Fréchet可微凸函数。我们引入惯性Douglas-Rachford DC算法和参数化惯性Douglas-Rachford DC算法来求解此类优化问题，并研究其收敛性。数值实验展示了所提算法在求解稀疏恢复和鲁棒分类问题时的表现，突出了其相较于现有同类算法的优越性能。
英文摘要
We propose two new Douglas-Rachford type algorithms for solving generalized DC programming problems. More precisely, we deal with the minimization of the sum of two possibly nonsmooth convex functions from which a Fréchet differentiable convex function with a Lipschitz continuous gradient is subtracted, in a Hilbertian framework. We introduce an inertial Douglas-Rachford DC algorithm and a parametrized inertial Douglas-Rachford DC algorithm for solving optimization problems of this type, and study their convergence behavior. Numerical experiments illustrate the behavior of the proposed algorithms when solving sparse recovery and robust classification problems, highlighting their superior performance in comparison with their state-of-the-art counterparts.
