I need to minimize the following L-infinity norm with respective to $\tau$. L-infinity norm of a matrix $A$ is defined as $\|A\| = max_{i,j}|a_{i,j}|$. 
$$
min_{\tau} \| I -S(S+\tau)^{-1}\|
$$

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

Any idea? Thanks.