Continuous Optimisation HT26, Optimisation terminology
Flashcards
Consider the optimisation model
\[\min _ {x \in \mathbb R^n} f(x) \quad\text{ subject to }x \in \mathcal F\]
@Define what is meant by a constrained local minimiser.
$x^\ast \in \mathcal F$ is a constrained local minimiser if $f(x^\ast) \le f(x)$ for all $x \in \mathcal F \cap B _ \varepsilon(x^\ast)$ for some $\varepsilon > 0$ (and hence $x^\ast$ may lie directly on a constraint).