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Descent methods for optimization on homogeneous manifolds

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  • Celledoni, Elena
  • Fiori, Simone

Abstract

In this article we present a framework for line search methods for optimization on smooth homogeneous manifolds, with particular emphasis to the Lie group of real orthogonal matrices. We propose strategies of univariate descent (UVD), methods. The main advantage of this approach is that the optimization problem is broken down into one-dimensional optimization problems, so that each optimization step involves little computation effort. In order to assess its numerical performance, we apply the devised method to eigen-problems as well as to independent component analysis in signal processing.

Suggested Citation

  • Celledoni, Elena & Fiori, Simone, 2008. "Descent methods for optimization on homogeneous manifolds," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1298-1323.
    • Handle: RePEc:eee:matcom:v:79:y:2008:i:4:p:1298-1323
    DOI: 10.1016/j.matcom.2008.03.013
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    Cited by:

    1. Jing Wang & Huafei Sun & Simone Fiori, 2019. "Empirical Means on Pseudo-Orthogonal Groups," Mathematics, MDPI, vol. 7(10), pages 1-20, October.
    2. Fiori, Simone, 2016. "A Riemannian steepest descent approach over the inhomogeneous symplectic group: Application to the averaging of linear optical systems," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 251-264.

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