barrier function

A term added to the objective that grows without bound as a point approaches a constraint boundary from inside.

For $g(x)\le0$ , the logarithmic barrier function is $B(x;\mu)=f(x)-\mu\ln(-g(x))$ , defined only where $-g(x)>0$ (strict feasibility). As $x$ approaches the boundary $g(x)=0$ from inside, the barrier term grows without bound, keeping any unconstrained solver started inside from ever crossing it.