I need to minimize the following L-infinity norm with respective to $\tau$

$$
min_{\tau} \| I -S(S+\tau)^{-1}\|
$$

$$
\text{subject to} \ S+\tau \ \text{is positive definite}
$$
where $S$ is symmetric but not full rank, $\tau$ is non-singular diagonal matrix. 

Any idea? Thanks.