AI 中文总结
研究非光滑非凸分布式优化问题，提出CADMM-Prox算法，它结合经典共识ADMM与近端机制，在局部目标函数半凸假设下可全局收敛至克拉克驻点邻域，相位检索实验显示其收敛行为更稳定。
AI 中文摘要
非光滑和非凸优化问题在机器学习、控制和信号处理中普遍存在，因其对稀疏解的需求以及许多目标函数固有的非凸性质。本文研究此类分布式优化问题，提出一种新颖的双层共识交替方向乘子法（ADMM）算法CADMM-Prox。该算法通过引入与外层变量相关的足够大的近端项，将经典共识ADMM与近端机制相结合。在局部目标函数为半凸的温和假设下，CADMM-Prox能全局收敛至克拉克驻点的邻域。相位检索问题的数值实验表明，与基线算法相比，该方法收敛行为更稳定。
英文摘要
Non-smooth and non-convex optimization problems are pervasive in machine learning, control, and signal processing, due to the need for sparse solutions and the inherently non-convex nature of many objective functions. In this paper, we study non-smooth and non-convex distributed optimization problems. We propose a novel bi-level Consensus Alternating Direction Method of Multipliers (ADMM) algorithm, termed CADMM-Prox. The proposed algorithm integrates classical Consensus ADMM with a proximal mechanism by introducing a sufficiently large proximal term associated with an outer-level variable. Under the mild assumption that the local objective functions are semi-convex, CADMM-Prox is guaranteed to converge globally to a neighborhood of a Clarke stationary point. Numerical experiments on a phase retrieval problem demonstrate that our proposed method exhibits more stable convergence behavior compared with baseline algorithm.
