论文标题
马鞍流动动力学：可观察的证书和可分离的正则化
Saddle Flow Dynamics: Observable Certificates and Separable Regularization
论文作者
论文摘要
本文提出了一个植根于可观察性的证书，即凸孔函数的马鞍流动动力学渐近收敛到鞍点。该可观察的证书直接弥合了LaSalle参数中不变集和平衡设置之间的差距，并概括了常规条件，例如严格的凸率 - concavity和近端正则化。我们进一步建立该证书，提出了一种可分离的正规化方法，用于鞍流动动力学，该方法对凸率造成的需求最少，但仍然可以保证渐近收敛到鞍点。我们的结果概括为通过对向量字段的预测进行预测，并立即应用作为线性程序的分布式解决方案。
This paper proposes a certificate, rooted in observability, for asymptotic convergence of saddle flow dynamics of convex-concave functions to a saddle point. This observable certificate directly bridges the gap between the invariant set and the equilibrium set in a LaSalle argument, and generalizes conventional conditions such as strict convexity-concavity and proximal regularization. We further build upon this certificate to propose a separable regularization method for saddle flow dynamics that makes minimal requirements on convexity-concavity and yet still guarantees asymptotic convergence to a saddle point. Our results generalize to saddle flow dynamics with projections on the vector field and have an immediate application as a distributed solution to linear programs.
