结合Barzilai-Borwein步长、非单调线搜索与外推的近端凸差算法
A proximal difference of convex functions algorithm using Barzilai-Borwein step size with nonmonotone line search and extrapolation
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中文总结 AI 辅助
本文提出结合Barzilai-Borwein步长、非单调线搜索与外推的近端凸差算法，证明其全局收敛性，经实验验证效率与精度优于现有DC算法。
中文摘要 AI 辅助
本文提出一种新型近端凸差（DC）算法框架，用于求解一般非凸、非光滑优化问题。通过将Barzilai-Borwein（BB）步长与非单调线搜索策略相结合，所提方法有效克服了标准近端DC算法固有的步长保守性与稳定性问题。此外，本文开发了外推机制以加速收敛，同时确保全局稳定性。在Kurdyka-Łojasiewicz性质下，严格证明了所提算法的全局收敛性。针对SCAD正则化最小二乘问题与图形Ginzburg-Landau图像分割模型的数值实验表明，与现有DC算法相比，所提方法具备极具竞争力的效率与精度。
英文摘要
The paper proposes a novel proximal difference-of-convex (DC) algorithmic framework to solve general non-convex, non-smooth optimization problems. By combining Barzilai-Borwein (BB) step sizes with nonmonotone line search strategies, our approach effectively overcomes the conservative step sizes and stability issues inherent in standard proximal DC algorithms. Furthermore, we develop extrapolation mechanisms to accelerate convergence while ensuring global stability. The global convergence of the proposed algorithms is rigorously established under the Kurdyka-Łojasiewicz property. Numerical experiments on the SCAD-regularized least squares problem and graphic Ginzburg-Landau image segmentation models demonstrate that the proposed methods achieve highly competitive efficiency and accuracy compared to existing DC algorithms.
