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& f_j(x) := x^\top A_j x + b_j^\top x + c_j \leq 0 \quad \text{ for all } j = 1, \dots, m,
\end{aligned}</math>
where all matrices ''A<sub>j</sub>'' are [[Positive semidefinite matrices|positive-semidefinite
We can apply path-following methods with the barrier
<math display="block">b(x) := -\sum_{j=1}^m \ln(-f_j(x)).</math> The function <math>b</math> is a self-concordant barrier with parameter ''M''=''m''. The Newton complexity is O(''(m+n)n''<sup>2</sup>), and the total runtime complexity is O(''m''<sup>1/2</sup> (m+n) ''n''<sup>2</sup>).
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