Solution
= Solution
On the strictly feasible region $c_i(x)>0$, the <logarithmic barrier> objective is
$$
\boxed{B_\mu(x)=f(x)-\mu\sum_{i=1}^m\log c_i(x).}
$$
With $y_i(x)=\mu/c_i(x)$, its <gradient> is
$$
\boxed{\nabla B_\mu(x)=g(x)-A(x)^Ty(x).}
$$
The positive coefficients $y_i$ are the barrier's multiplier estimates.