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arXiv · 2202.07821

A Projected Subgradient Method for the Computation of Adapted Metrics for Dynamical Systems

Maurício Louzeiro·Christoph Kawan·Sigurdur Hafstein·Peter Giesl·Jinyun Yuan
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Abstract

In this paper, we extend a recently established subgradient method for the computation of Riemannian metrics that optimizes certain singular value functions associated with dynamical systems. This extension is threefold. First, we introduce a projected subgradient method which results in Riemannian metrics whose parameters are confined to a compact convex set and we can thus prove that a minimizer exists; second, we allow inexact subgradients and study the effect of the errors on the computed metrics; and third, we analyze the subgradient algorithm for three different choices of step sizes: constant, exogenous and Polyak. The new methods are illustrated by application to dimension and entropy estimation of the H\'enon map.

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Maurício Louzeiro, Christoph Kawan, Sigurdur Hafstein, Peter Giesl, Jinyun Yuan. 2022-02-16. A Projected Subgradient Method for the Computation of Adapted Metrics for Dynamical Systems. https://arxiv.org/abs/2202.07821

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