Self-concordant function

Self-concordant function

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

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

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

Properties

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

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 functions used in interior point methods for convex and nonlinear optimization.


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