Based on first-order Taylor series expansion around current trial solution 1. Evaluate partial derivatives $ c_j = \frac{\partial f}{\partial x_j} \quad \text{at } \mathbf{x} = \mathbf{x}^{k-1} $ 2. Formulate LP problem using partial derivatives as objective function coefficients $ \begin{alignat}{3} \text{max} \quad &&& \mathrlap{g(\mathbf{x}) = \sum_{j=1}^nc_jx_j}\\ \text{s.t.} \quad &&&& \mathbf{Ax} &\leq b\\ &&&& \mathbf{x} &\geq 0 \end{alignat} $ Optimal solution called $\mathbf{x}_{LP}^{(k)}$ 3. Introduce variable $t(0 \leq t \leq 1)$, use: $ \mathbf{x} = \mathbf{x}^{(k-1)}+t\big(\mathbf{x}_{LP}^{(k)}-\mathbf{x}^{(k-1)}\big) $ Plug $\mathbf{x}$ into original objective function $f{\mathbf{x}}$, differentiate wrt $t$, set equal to zero