Applied Analysis Seminar

**Tuesday July 23
in K9509, SFU
**

**Speaker and Title:**
2:00 - 2:45: W. Hare (SFU)
"Identifing Manifolds for Partially Smooth Functions"

**Abstract:**
Given a weak set of demands we show that manifolds
associated with Partially Smooth functions can be identified in a finite
number of steps.

**Speaker and Title:**
2:45 - 3:30: Adrian Lewis (SFU)
"Robust regularization in optimization"

**Abstract:**
Suppose we want to minimize a function that is evaluated not
at the point we choose, but rather at an unpredictably
perturbed point. In other words, we want to minimize
a ``robust regularization'': at any point, this
regularization equals the maximum value of the function in a
fixed neighbourhood of the point. For example, a crucial
function in feedback control is the spectral abscissa of a
square matrix (the largest real part of an eigenvalue). Its
robust regularization is the ``pseudospectral absicssa'',
a useful tool in robust control. I will describe conditions
guaranteeing that the robust regularization is locally
Lipschitz even when the underlying function is not, and
apply this result to the pseudospectral abscissa.