Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, School of Electronic and Information Engineering, Southwest University, Chongqing 400715, China.
Department of Mathematics, Texas A&M University at Qatar, Doha 23874, Qatar.
Neural Netw. 2022 Nov;155:592-601. doi: 10.1016/j.neunet.2022.09.013. Epub 2022 Sep 17.
This paper develops two neurodynamic approaches for solving the L-minimization problem with the linear inequality constraints. First, a centralized neurodynamic approach is proposed based on projection operator and nonnegative quadrant. The stability and global convergence of the centralized neurodynamic approach are analyzed by the Lyapunov method in detail. Considering that the distributed optimization problem has the advantages of information protection and scalability, the L-minimization problem with linear inequality constraints is transformed into a distributed sparse optimization problem under mild conditions. Then, using the centralized neurodynamic approach and multi-agent consensus theory, a distributed neurodynamic approach is proposed for the distributed optimization problem. Furthermore, relevant theories show that each agent globally converges to an optimal solution of the distributed optimization problem. Finally, the presented centralized neurodynamic approach is applied to sparse recovery problem with L-norm noise constraints and the effectiveness of distributed approach is shown by several experiments on sparse signal recovery.
本文提出了两种神经动力学方法来解决具有线性不等式约束的 L 极小化问题。首先，基于投影算子和非负象限提出了一种集中式神经动力学方法。通过详细的 Lyapunov 方法分析了集中式神经动力学方法的稳定性和全局收敛性。考虑到分布式优化问题具有信息保护和可扩展性的优点，在线性不等式约束下，将 L 极小化问题转化为在温和条件下的分布式稀疏优化问题。然后，利用集中式神经动力学方法和多智能体一致性理论，针对分布式优化问题提出了一种分布式神经动力学方法。此外，相关理论表明，每个智能体全局收敛到分布式优化问题的最优解。最后，将提出的集中式神经动力学方法应用于具有 L-范数噪声约束的稀疏恢复问题，并通过稀疏信号恢复的几个实验展示了分布式方法的有效性。
