Imagine, I have a symmetric matrix $B$. I want a set of rows for which I can get the maximum from the least value of all rows. For example if $B=\left(\begin{smallmatrix}- & 3& 4\\3& -& 6\\ 4 &6& -\end{smallmatrix}\right)$, then $3$ is the least value for row $1$, $3$ for row $2$, and $4$ for row $3$. Among these only row $1$ and row $2$ have the maximum value (i.e. $3$). So, I want to express this mathematically. So far I got this:
$\underset{i\in\{1,\dots,S\}}{\operatorname{argmax}}\bigl(\min\limits_{\substack{i\neq j\,\\j\in\{1,\dots,S\}}} ({B_{ij}})\bigr)$