附加结构单调包含的二次分裂动力学与消失阻尼
Radu Ioan Boţ1, David Alexander Hulett1
1Faculty of Mathematics, University of Vienna, Vienna, Austria.
Journal of dynamics and differential equations
|March 4, 2024
概括
本研究介绍了一种新的分割系统,用于在希尔伯特空间中找到运算符零. 该方法确保了解决方案的融合和快速减速,在凸起式优化中的应用.
科学领域:
- 优化理论 优化理论
- 功能分析是一种功能分析.
- 数字分析 数字分析
背景情况:
- 解决了为最大单调和强制性运算符的和找到零的挑战.
- 通过引入一种新的二级动态系统,以消失的阻尼,以现有方法为基础.
研究的目的:
- 分析由时间依赖的前向后向分割系统产生的轨迹的非对称行为.
- 为了确定运算方程的解决方案集的轨迹的弱收.
- 为了证明速度到零的快速收.
主要方法:
- 使用二级动态系统,具有消失式阻尼.
- 雇佣了一个时间依赖的前向后向分割操作员.
- 在一个真实的希尔伯特空间框架中分析系统的行为.
主要成果:
- 证明了生成的轨迹对A + B的零集的弱收.
- 证明轨迹的速度迅速汇聚到零点.
- 作为特殊情况,为特定的凸式优化问题推导出快速收率.
结论:
- 拟议的分割系统是有效的寻找单调和强制性运算符的和的零.
- 该系统提供了对收和快速减速的理论保证.
- 数值实验验证实了理论发现,并证明了实际应用.
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