I am an applied mathematician interested in the application of optimization to problems in system identification and design under uncertainty. My current work with Paul focuses on constructing ridge approximations of expensive quantities of interest using only function values and then exploiting the structure of these approximations to solve chance constrained design problems. My thesis work centered on solving a large nonlinear least squares problem by projecting onto a low-dimensional subspace of the meas
The Lipschitz matrix generalizes the notion of Lipschitz continuity by pulling the scalar Lipschitz constant inside the norm, promoting it to a matrix. Whereas a scalar Lipschitz function $ f\in \set L(\set D, L)$ satisfies $$ \set L(\set D, L) := \lbrace f:\set D\to \R: |f(\ve x_1) - f(\ve x_2) | \le L\| \ve x_1 - \ve x_2\|_2 \ \forall \ve x_1, \ve x_2 \in \set D \rbrace, $$ a matrix Lipschitz function $f\in \set L(\set D, \ma L)$ satisfies $$ \set L(\set D, \ma L) := \lbrace f:\set D\to \R: |f(\ve x_1) -
An inverse eigenvalue problem seeks to infer properties of a system through its eigenvalues. A classic example is Kac's question: Can one hear the shape of a drum? ; the answer turns out to be no in two dimensions . In this paper we develop a version of this problem accessible to undergraduates in a matrix analysis course. Here we consider the case of a beaded string where the beads are symmetrically distributed around the mid-point of the string. Using classical results of Gantmacher, Krein, and others, we