Logarithmically homogeneous barrier
= Logarithmically homogeneous barrier
{title2=$F(ts)=F(s)-\nu\log t$}
A cone barrier with this scaling law satisfies $\langle\nabla F(s),s\rangle=-\nu$ and $\nabla F(ts)=t^{-1}\nabla F(s)$. Therefore a <central path> with $y=-\mu\nabla F(s)$ has primal-dual gap $\nu\mu$. A product of orthant and <Lorentz cone> canonical barriers adds their parameters.