A spectral function on a formally real Jordan algebra is a real-valued function which depends only on the eigenvalues of its argument. One convenient way to create them is to start from a function f : IRr - IR which is symmetric in the components of its argument, and to define the function F(u)...

We extend the powerful smoothing techniques of Yu. Nesterov to the framework of Euclidean Jordan algebras. This study allows us to design a new scheme for minimizing the largest eigenvalue of an affine function on a Euclidean Jordan algebra. We prove that its complexity is in the order of O...