Saddle Flow Dynamics: Observable Certificates and Separable Regularization

Pengcheng You; Enrique Mallada

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arXiv · 2009.14714

Saddle Flow Dynamics: Observable Certificates and Separable Regularization

Pengcheng You·Enrique Mallada

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Abstract

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.

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Pengcheng You, Enrique Mallada. 2020-09-30. Saddle Flow Dynamics: Observable Certificates and Separable Regularization. https://arxiv.org/abs/2009.14714

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