Descent methods for optimization on homogeneous manifolds

Authors:
Elena Celledoni;Simone Fiori
Affiliations:
Department of Mathematical Sciences-Faculty of Information Technology, Mathematics and Electrical Engineering, Norwegian University of Science and Technology (NTNU), Alfred Getz vei 1, NO-7491 Tro ...;Dipartimento di Elettronica, Intelligenza Artificiale e Telecomunicazioni (DEIT), Facoltí di Ingegneria, Universití Politecnica delle Marche, Via Brecce Bianche, I-60131 Ancona, Italy
Venue:
Mathematics and Computers in Simulation
Year:
2008

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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.