Add a barrier function to objective to keep it from leaving the feasible solution area - want terms of barrier function to be small - grows larger as approaches solution boundaries - *r* acts as weight for penalty function - increases if solution is near boundary # Example $ \begin{alignat*}{3} \text{mat} \quad &&& \mathrlap{-x_1^2+2x_1-x_2^2+3x_2} \\ \text{s.t.}\quad &&&& x_1+x_2&\leq2 \\ &&&& x_1, x_2&\geq0 \end{alignat*} $ Rewrite as: $ P(x, r) = -x_1^2+2x_1-x_2^2+3x_2-r\bigg(\frac{1}{2-x_1-x_2}+\frac{1}{x_1}+\frac{1}{x_2}\bigg) $