Optimization on manifolds: methods and applications

Prof. Pierre-Antoine Absil (Universite catholique de Louvain (Louvain-la-Neuve, Belgium))

MSI Computational Mathematics Seminar Series

DATE: 2009-01-30
TIME: 11:00:00 - 12:00:00
LOCATION: JD G35
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ABSTRACT:
In this talk, we are interested in applications of differential geometry in optimization. They arise when the optimization problem can be formulated as finding an optimum of a real-valued cost function defined on a smooth nonlinear search space. Oftentimes, the search space is a "matrix manifold", in the sense that its points admit natural representations in the form of matrix arrays. In most cases, the nonlinearity of the manifold is due either to matrix orthogonality constraints in the search space, or to invariance properties in the cost function that need to be factored out in order to obtain a nondegenerate optimization problem.

In the recent years, the importance of optimization problems on manifold has stimulated the development of geometric optimization algorithms that exploit the differential structure of the manifold search space. In this talk, we give an overview of geometric optimization algorithms and their applications, with an emphasis on the underlying geometric concepts and on the numerical efficiency of the algorithm implementations.
BIO:
Pierre-Antoine Absil is an associate professor in the Departement of Mathematical Engineering of the Universite catholique de Louvain (Louvain-la-Neuve, Belgium). Previously, he has held positions at the University of Liege, Florida State University, and the University of Cambridge. He has also been a visitor with Monash University, the University of Wurzburg, and Sandia National Laboratories.

Dr Absil's major research area is numerical optimization, with particular interests in numerics on manifolds, linear and nonlinear programming algorithms, and biomedical applications. He is co-author with Robert Mahony and Rodolphe Sepulchre of the recent book "Optimization Algorithms on Matrix Manifolds". http://www.inma.ucl.ac.be/~absil/