Radially unbounded function

In mathematics, a radially unbounded function is a function $f: \mathbb{R}^n \rightarrow \mathbb{R}$ for which

Such functions are applied in control theory and required in optimization for determination of compact spaces.

Notice that the norm used in the definition can be any norm defined on $\mathbb{R}^n$ , 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:

单词	Radially unbounded function
释义	Radially unbounded function 英语百科 Radially unbounded function In mathematics, a radially unbounded function is a function $f: \mathbb{R}^n \rightarrow \mathbb{R}$ for which Such functions are applied in control theory and required in optimization for determination of compact spaces. Notice that the norm used in the definition can be any norm defined on $\mathbb{R}^n$ , 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:
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