Optimality condition for a convex, unconstrained problemConsider the unconstrained optimization problem \[ \min_x \: f_0(x) , \] where \(f_0 : \mathbf{R}^n \rightarrow \mathbf{R}\) is convex and differentiable. \[ \forall \: y \in \mathbf{X} : \nabla f_0(x) ^T (y-x) \ge 0 . \] where the feasible set \(\mathbf{X}\) is now the whole space \(\mathbf{R}^n\), reduces to \[ \nabla f_0(x) = 0. \] Example: |