2Characterizing solutions

Introduction¶

In this chapter, we consider optimization problems of the form

where $f_0 : \mathbb{R}^n \to \mathbb{R}$ is the objective function. For simplicity, we assume (unless otherwise stated) that the domain of (1) is $\mathcal{D} = \mathbb{R}^n$. Therefore the constraint set $\Omega$ and feasible set $\mathcal{F}$ coincide.

Recall from the previous chapter that when $\Omega = \mathbb{R}^n$ the problem (1) the problem is said to be unconstrained; otherwise, if $\Omega \subset \mathbb{R}^n$, we say that (1) is a constrained optimization problem.