 
Summary: 20 Nov 2009 Tech. Report UCLINMA2009.043
Optimization On Manifolds: Methods And
Applications
P.A. Absil1
D´epartement d'ing´enierie math´ematique, Universit´e catholique de Louvain, B1348
LouvainlaNeuve, Belgium http://www.inma.ucl.ac.be/~absil/
1 Introduction
This paper is written as an invitation to the area of optimization on mani
folds. It follows quite closely the structure of the plenary talk given at the 14th
BelgianFrenchGerman Conference on Optimization, Leuven, 1418 Septem
ber 2009. The style is rather on the informal side, and there is a definite bias
towards the exposition given in the monograph [5], to which we refer for more
details and for a larger bibliography. When we cite [5], we do not imply that it
is the original reference for the topic in question; for a historical perspective,
the reader is invited to consult the "Notes and References" sections.
The general problem of optimization on manifolds is introduced in Sec
tion 2. A motivation for considering the problem in its most abstract form
is given in Section 3. Manifolds are defined in more technical terms in Sec
tion 4. Several specific manifolds are presented in Section 5, along with point
ers to applications where they are involved. Section 6 describes a steepest
