1.2.1 Unconstrained optimization

The term ``unconstrained optimization" usually refers to the situation where all points $x$ sufficiently near $x^*$ in $\mathbb{R}^n$ are in $D$ , i.e., $x^*$ belongs to $D$ together with some $\mathbb{R}^n$ -neighborhood. The simplest case is when $D=\mathbb{R}^n$ , which is sometimes called the completely unconstrained case. However, as far as local minimization is concerned, it is enough to assume that $x^*$ is an interior point of $D$ . This is automatically true if $D$ is an open subset of $\mathbb{R}^n$ .