= Central path
{title2=$\mu>0$}
For a strictly feasible primal-dual <conic optimization> problem and a logarithmically homogeneous barrier, the central path consists of solutions
$$
s=Ax-b\in\operatorname{int}K,\quad A^\top y=c,\quad y\in\operatorname{int}K^*,\quad y=-\mu\nabla F(s),\quad\mu>0.
$$
The primal-dual gap is $\langle s,y\rangle=\nu\mu$. Existence requires appropriate feasibility and boundedness hypotheses, rather than merely a full-rank constraint matrix. Linearizing these equations gives a <central-path Newton system>.
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