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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$ .


Daniel 2010-12-20