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20 Nov 2009 Tech. Report UCL-INMA-2009.043 Optimization On Manifolds: Methods And

Summary: 20 Nov 2009 Tech. Report UCL-INMA-2009.043
Optimization On Manifolds: Methods And
P.-A. Absil1
D´epartement d'ing´enierie math´ematique, Universit´e catholique de Louvain, B-1348
Louvain-la-Neuve, 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
Belgian-French-German 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-


Source: Absil, Pierre-Antoine - Département d'ingénierie Mathématique, Université Catholique de Louvain


Collections: Mathematics