Descent methods for optimization on homogeneous manifolds

被引：12

作者：

Celledoni, Elena ^{[1
]}

Fiori, Simone ^{[2
]}

机构：

[1] Norwegian Univ Sci & Technol, Dept Math Sci, Fac Informat Technol Math & Elect Engn, NO-7491 Trondheim, Norway

[2] Univ Politecn Marche, Fac Ingn, Dipartimento Elettron Intelligenza Artificiale, I-60131 Ancona, Italy

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2008年 / 79卷 / 04期

关键词：

Optimization on manifolds; Lie group actions; Eigen-problems; Independent component analysis; Signal processing;

D O I：

10.1016/j.matcom.2008.03.013

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

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. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：1298 / 1323

页数：26

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