Seminar Details
2006-03-07 (14.00 pm) : "Smoothing techniques on Jordan algebras"
At Euler building
Organized by Mathematical Engineering
Speaker :
Michel Baes (CORE)
Abstract :
A spectral function on a formally real Jordan algebra is a
real-valued function that depends only on the eigenvalues of its
argument. One convenient way to create them is to start from a
function $f$ from $\mathbb{R}^r$ to $\mathbb{R}$ that is symmetric in the components
of its argument, and to define the function $F(u):=f(\lambda(u))$ where $\lambda(u)$ is
the vector of eigenvalues of $u$. A particular example of this construction is
given by functions of symmetric matrices that only depend on the
eigenvalues of its argument. We positively answer an open question proposed in the PhD thesis
of H. Sendov : "is it possible to compute the hessian of spectral functions on Jordan algebras?"
We then exploit this result to investigate how the power smoothing
techniques of Yu. Nesterov can in some instances be extended to
Jordan algebras. In particular, we propose a new algorithm to
minimize a sum of Euclidean norms and we perform its complexity
analysis.