Self-concordant

In optimization, a self-concordant function is a function ${\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} }$ for which

or, equivalently, a function ${\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} }$ that, wherever ${\displaystyle f''(x)>0}$, satisfies

and which satisfies ${\displaystyle f'''(x)=0}$ elsewhere.

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