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Mathematics > Optimization and Control

arXiv:1412.2841 (math)
[Submitted on 9 Dec 2014]

Title:Optimization Methods on Riemannian Manifolds via Extremum Seeking Algorithms

Authors:Farzin Taringoo, Peter M. Dower, Dragan Nesic, Ying Tan
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Abstract:This paper formulates the problem of Extremum Seeking for optimization of cost functions defined on Riemannian manifolds. We extend the conventional extremum seeking algorithms for optimization problems in Euclidean spaces to optimization of cost functions defined on smooth Riemannian manifolds. This problem falls within the category of online optimization methods. We introduce the notion of geodesic dithers which is a perturbation of the optimizing trajectory in the tangent bundle of the ambient state manifolds and obtain the extremum seeking closed loop as a perturbation of the averaged gradient system. The main results are obtained by applying closeness of solutions and averaging theory on Riemannian manifolds. The main results are further extended for optimization on Lie groups. Numerical examples on Riemannian manifolds (Lie groups) SO(3) and SE(3) are presented at the end of the paper.
Subjects: Optimization and Control (math.OC)
Cite as: arXiv:1412.2841 [math.OC]
  (or arXiv:1412.2841v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1412.2841

Submission history

From: Farzin Taringoo [view email]
[v1] Tue, 9 Dec 2014 02:59:58 UTC (579 KB)
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