Radially unbounded function: Difference between revisions

Revision as of 00:11, 16 July 2017

Revision as of 02:23, 17 December 2020

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:<math>\|x\| \to \infty \Rightarrow f(x) \to \infty. </math>

Or symbolically,

:<math>\forall L >0:\exists a > 0 : \forall x \in \mathbb{R}^n:\Vert x \Vert > a \Rightarrow f(x) > L</math>

Such functions are applied in [[control theory]] and required in [[Mathematical optimization|optimization]] for determination of [[compact space]]s.