Radially unbounded function: Difference between revisions

Revision as of 19:35, 27 April 2015

Revision as of 08:29, 2 August 2015

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

Such functions are applied in [[control theory]] and required in [[Mathematical_optimization|optmizationoptimization]] for determination of [[compact_space|compact spaces]].

Notice that the norm used in the definition can be any norm defined on <math> \mathbb{R}^n </math>, and that the behavior of the function along the axes does not necessarily reveal that it is radially unbounded or not; i.e. to be radially unbounded the condition must be verified along any path that results in: