Friday, July 11, 2008 3:30 pm
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4:30 pm
EDT (GMT -04:00)
On the structure of binary matroids
Speaker: | Bert Gerards |
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Affiliation: | CWI, Netherlands |
Room: | Mathematics & Computer Building (MC) 5158 |
Abstract:
Given a separable strongly self-concordant function $f:\R^n \rightarrow \R$, we show the associated spectral function $F(X)= (f \circ \lambda)(X)$ is also strongly self-concordant function. In addition, there is a universal constant $\mathcal{O}$ such that, if $f(x)$ is separable self-concordant barrier then $\mathcal{O}^2F(X)$ is a self-concordant barrier. We estimate that for the universal constant we have $\mathcal{O} \le 22$. This generalizes the relationship between the standard logarithmic barriers $-\sum_{i=1}^n\log x_i$ and $-\log \det X$ and gives a partial solution to a conjecture of L. Tunçel.
This is a joint work with Javier Peña, Carnegie Mellon University.