分布神经动力学模型用于解决一类非线性方程系统
IEEE transactions on neural networks and learning systems
|November 13, 2023
概括
本研究介绍了三种新的分布式神经动力学模型 (DNMs),用于解决非线性方程系统 (SNEs). 这些模型展示了全球趋同,并为二次编程问题提供了有效的解决方案.
科学领域:
- * 计算数学和动态系统.
- * 人工智能和机器学习.
- * 优化理论.
背景情况:
- * 非线性方程系统 (SNEs) 是各种科学和工程学科的基础.
- *现有的解决SNE的方法往往面临着融合和效率的挑战,特别是在复杂或大规模的问题上.
- *分布式神经动力学模型 (DNMs) 提供了一种有前途的方法来解决SNE,因为它们固有的并行性和自适应性学习能力.
研究的目的:
- * 提出和分析三种用于解决非线性方程系统的新型分布式神经动力学模型 (DNMs).
- * 调查这些DNM的收性质和有效性,包括精确和最小平方的解决方案.
- * 证明拟议的DNM在解决二次编程 (QP) 问题的实际适用性.
主要方法:
- * 开发DNM-I:一个双层模型,将动态正定量矩阵与初级-双元方法相结合,证明全球收.
- * 开发DNM-II:一个简洁的单层模型,利用动态正定数矩阵,时间变化的增益和激活函数,确保全球趋同.
- *DNM-III的开发:基于DNM-II的精细单层模型,包含时间变化的增益和激活功能,用于全球固定时间共识和趋同,具有已证明的指数趋同 (平滑情况) 和有限时间趋同 (非平滑情况).
主要成果:
- * DNM-I 已被证明是全球趋同的.
- * DNM-II是以简洁的结构和全球趋同来开发的.
- * DNM-III表现出全球固定的时间共识和趋同,在平滑情况下在Polyak-Łojasiewicz (PL) 条件下具有全球指数趋同,在不平滑情况下在Kurdyka-Łojasiewicz (KL) 条件下具有全球有限时间趋同.
- * 提出的DNM已成功应用于解决二次编程 (QP) 问题,数值示例验证了它们的有效性.
结论:
- * 提出的分布式神经动力学模型 (DNM) 为非线性方程系统 (SNE) 提供了有效和融合的解决方案.
- * DNM-III提供了增强的收特性,包括固定时间和有限时间的收,用于光滑和不光滑的问题.
- *将这些DNM应用到二次编程中,证明了它们的实际实用性和相对于现有方法的优势.
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