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I have a question about the degeneracy of the analytic center of a set of linear inequalities.

When the set of linear inequalities is degenerate, I guess that the analytic center would also be degenerate.

I think that this is an example

$$ \begin{cases} x_1+x_2+x_3+x_4\leq 4\\ 3x_1+x_2+x_3+x_4\leq 6 \end{cases} $$

I guess people have worked on this before and I hope some references could be pointed out.

Thanks!

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