Recall optimization (math). An optimization (math) problem is convex if: the objective is convex function inequality constrains’ functions are convex equality constrains are affine Special convex problems Linear Program Optimality Criterion for Differentiable Objective x is optimal IFF its feasible and
\begin{equation} \nabla f_{0} \left(x\right)^{T} \left(y-x\right) \geq 0 \end{equation}
for all feasible y. examples unconstrained problem: x minimizes f_{0}\left(x\right) IFF \nabla f_{0}\left(x\right) = 0 equality constrained problem: x minimizes f_{0}\left(x\right) subject to Ax = b IFF there is a v such that Ax = b, \nabla f_{0}\left(x\right) + A^{T}v = 0 Local and Global Optima Any locally optimal point of a convex problem is globally optimal.