Convex Optimization

Definition

$\underset{x}{\min }f(x)$ subject to $g(x)\le 0,h(x)=0$

An optimization problem in which the objective function is a Convex Function and the feasible set is a Convex Set.

Facts

Every local minimum is a global minimum

The convex feasible set condition is equivalent to the following conditions

• the inequality constraint function $g$ is a Convex Function
• the equality constraint function $h$ is an affine function