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Minimize L-infinity norm with restrictions.

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.