Trisha Shetty (Editor)

Self concordant function

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In optimization, a self-concordant function is a function f : R R for which

Contents

| f ( x ) | 2 f ( x ) 3 / 2 .

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

History

The self-concordant functions are introduced by Yurii Nesterov and Arkadi Nemirovski in their 1994 book.

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.

References

Self-concordant function Wikipedia