Self-concordant function: Difference between revisions

Revision as of 20:27, 13 April 2017

Revision as of 20:36, 13 April 2017

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: <math>|f'''(x)| \leq 2 f''(x)^{3/2}</math>

or, equivalently, a function <math>f:\mathbb{R} \rightarrow \mathbb{R}</math> that, wherever <math>f''(x) \neq> 0</math>, satisfies

: <math>\left| \frac{d}{dx} \frac{1}{\sqrt{f''(x)}} \right| \leq 1</math>

and which satisfies <math>f'''(x) = 0</math> wherever <math>f''(x) = 0</math>elsewhere.

A function <math>g(x) : \mathbb{R}^n \rightarrow \mathbb{R}</math> is self-concordant if its restriction to any arbitrary line is self-concordant. <ref>{{cite book