arXiv cs.MA· Juntao Li, Qihang Guo, Deyuan Meng·· 11 小时前AI 评分18
面向分布式 SCAD 正则化稀疏最小二乘的双层神经动力学方法
A Bilevel Neurodynamic Approach for Distributed SCAD-Regularized Sparse Least Squares
AI 导读
针对 SCAD 惩罚非光滑非凸、现有分布式神经动力学方法难以直接扩展的问题，研究者提出一种双层 PSO-神经动力学方法，可全局最优求解分布式 SCAD 正则化稀疏最小二乘。
正文 · 原文
Abstract:This paper proposes a bilevel particle swarm optimization (PSO)-neurodynamic method for solving the distributed sparse least-squares problem regularized by the smoothly clipped absolute deviation (SCAD) penalty to global optimality. The SCAD penalty is nonsmooth and nonconvex, so existing distributed neurodynamic methods have not been extended to it directly. Through two-time-scale singular perturbation analysis, a rigorous full-trajectory convergence theory with explicit convergence rates is established for the inner collaborative multi-agent neurodynamic system without requiring the second-order sufficient condition. A theory-guided inner-outer collaborative optimization framework is further developed, in which a red-light green-light sensitivity mechanism is embedded in the outer PSO search to enhance global search while concentrating computational effort on the SCAD shape parameters, thereby improving recovery accuracy and computational efficiency. Simulation results on four sparse-recovery scenarios demonstrate that the proposed method accurately recovers the true sparsity pattern and achieves faster convergence and lower relative error than competing neurodynamic methods.
| Subjects: | Optimization and Control (math.OC); Multiagent Systems (cs.MA) |
| Cite as: | arXiv:2611.07618 [math.OC] |
| (or arXiv:2611.07618v1 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2611.07618 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Juntao Li [view email]
[v1]
Thu, 5 Nov 2026 08:01:08 UTC (3,583 KB)
来源：arXiv cs.MA · arxiv.org