Self-concordant function

From Wikipedia, the free encyclopedia

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

|f'''(x)| \leq 2 f''(x)^{3/2}.

A function g(x) : \mathbb{R}^n \rightarrow \mathbb{R} is self-concordant if its restriction to any arbitrary line is self-concordant.

[edit] Properties

Self concordance is preserved under addition, affine transformations, and scalar multiplication by a value greater than one.

[edit] Applications

Among other things, self-concordant functions are useful in the analysis of Newton's method. Self-concordant barrier functions are used to develop the barrier method for convex optimization.

This applied mathematics-related article is a stub. You can help Wikipedia by expanding it.