Optimization Algorithms on Matrix Manifolds

P.-A. Absil, R. Mahony, and R. Sepulchre

Princeton University Press

Contents Talks Events Software Bibtex Authors Publisher's page Catalog links Errata

1. Introduction
2. Motivation and applications
3. Matrix manifolds: first-order geometry
4. Line-search algorithms
5. Matrix manifolds: second-order geometry
6. Newton's method
7. Trust-region methods
8. A constellation of superlinear algorithms
Detailed table of contents

Chapter One

Selected related talks

Slides of the BFG'09 talk "Optimization on manifolds: methods and applications", Leuven, 18 Sep 2009
Talk on vector transport given at ICIAM 07, 17 July 2007: PDF file.
Overview talk given at the DYSCO meeting, 16 April 2007: PDF file.

Related events

Invited session on Optimization on Manifolds at Optimization 2011
EECI graduate course on Optimization on Matrix Manifolds, Supelec (Paris), 14-17 February 2011
29th International Summer School in Automatic Control of Grenoble: "Optimization on manifolds: theory and applications", Grenoble, France, 16-19 September 2008.
Pre-conference workshop on Optimization on Manifolds at the 46th IEEE Conference on Decision and Control, New Orleans, 11 December 2007.
Course on Optimization on Manifolds at the Belgian Graduate school in Systems, Optimization, Control and Networks, Louvain-la-Neuve, October 2007.

Related software

GenRTR, by Chris Baker, Pierre-Antoine Absil, and Kyle Gallivan: the Generic Riemannian Trust-Region package. GenRTR is a MATLAB package for the optimization of functions defined on Riemannian manifolds.
SG_MIN, by Ross Lippert: a set of MATLAB routines for doing optimization on Stiefel and Grassmann manifolds.

Bibtex entry

@BOOK{AbsMahSep2008,
 author = "P.-A. Absil and R. Mahony and R. Sepulchre",
 title = "Optimization Algorithms on Matrix Manifolds",
 publisher = "Princeton University Press",
 address = "Princeton, NJ",
 year = 2008,
 pages = "xvi+224",
 isbn = "978-0-691-13298-3",
}

About the authors

P.-A. Absil is with the Department of Mathematical Engineering, Université catholique de Louvain.
R. Mahony is with the Department of Engineering, The Australian National University.
R. Sepulchre is with the Department of Electrical Engineering and Computer Science, Université de Liège.