Convex Optimization¶

A mathematical optimization is convex if the objective is a convex function and the feasible set is a convex set. The standard form of a convex optimization problem is:

\[\begin{split}\begin{align*} \text{minimize } & f_0(x) \\ \text{subject to } & f_i(x) \leq 0,\ i=1,\ldots,m \\ & h_i(x) = 0,\ i=1,\ldots,p \end{align*}\end{split}\]