= Conic phase-I problem
An auxiliary conic optimization problem searches for strict feasibility before following a <central path>. Given $e\in\operatorname{int}K$, minimizing $t$ subject to $Ax-b+te\in K$ and $t\geq-1$ has a strict feasible start for sufficiently large $t$. Any feasible solution with $t<0$ certifies $Ax-b\in\operatorname{int}K$. If the original problem is strictly feasible, a small negative $t$ is feasible. Equality constraints and dual feasibility require their corresponding auxiliary procedures.
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