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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.

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    $\begingroup$ Can you please clarify what you mean by the L-infinity norm of a matrix? Do you mean the operator norm with respect to the Euclidean norm on the vector space? $\endgroup$
    – Yemon Choi
    Oct 25, 2015 at 0:54
  • $\begingroup$ Thanks. I edit my problem to make it more clear. Now L-infinity norm of a matrix is the largest absolute value of a entry in the matrix. $\endgroup$
    – phil wang
    Oct 25, 2015 at 13:15

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