一个原始双动态系统的时间重新缩放,具有异常消失的阻尼
David Alexander Hulett1, Dang-Khoa Nguyen1
1Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
Applied mathematics and optimization
|June 5, 2023
概括
本研究引入了一种新的二次动态系统,用于凸函数最小化,实现初级-双元差距,可行性和客观价值的快速融合. 系统 系统 系统
科学领域:
- 优化理论 优化理论
- 凸的分析 凸的分析
- 动态系统 动态系统
背景情况:
- 在线性约束下最小化凸函数是优化的一个基本问题.
- 现有的二级动态系统提供了趋同,但可能缺乏可调节的参数来提高速度.
研究的目的:
- 开发和分析一个修改后的二阶动态系统,用于用线性等式约束对凸最小化.
- 调查时间调整参数对汇率的影响.
- 为原始-双重轨迹建立理论趋同保证.
主要方法:
- 制定一个二阶动态系统与一个非对称地消失的缓冲术语.
- 分析系统的轨迹,使用趋同率分析.
- 对初级-双元解决方案的弱收性质的研究.
- 数字实验与现有的动态系统进行比较.
主要成果:
- 证明了初级-双元差距,可行性测量和客观函数值的快速收.
- 确定收率取决于时间调整参数,允许潜在的改进.
- 在利普希茨梯度条件下,证明了初级-双重轨迹的弱无边际收到最佳解决方案.
- 对初级梯度和双辅助运算符的收率有所改善.
结论:
- 拟议的时间重新缩放的二次动态系统为凸优化提供了一种有效和可改进的方法.
- 通过重新调整参数调整收率的能力提供了实际优势.
- 数字结果验证了理论发现,并突出了系统的性能与替代品相比.
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