Seminar Details
2005-12-06 (14.00 pm) : Colloquium CESAME/MAPA : Optimization on Manifolds
At Auditoire Euler
Organized by Mathematical Engineering
Speaker :
Absil, Pierre-Antoine
Abstract :
It is well known that several matrix computation problems
can be recast as finding local or global optimizers of a cost function
whose domain is not a linear space, but can nevertheless be endowed
with a manifold structure (that is, it admits local coordinate systems
that are "compatible"). We will see how this manifold structure can be
exploited in order to define and analyse optimization algorithms such
as the Newton method and the conjugate gradients method. In particular,
we will see how these optimization methods, when applied to computing
eigenvalues of a symmetric matrix, lead to competitive numerical
algorithms that also shed a new light on existing algorithms.