Self-Scaled Barriers for Irreducible Symmetric Cones

Self-Scaled Barriers for Irreducible Symmetric Cones

Self{scaled barrier functions are fundamental objects in the theory of interior{point methods for linear optimization over symmetric cones, of which linear and semideenite programming are special cases. We are classifying all self{scaled barriers over irreducible symmetric cones and show that these functions are merely homothetic transformations of the universal barrier function. Together with ...

Numerical Analysis Reports SELF–SCALED BARRIERS FOR IRREDUCIBLE SYMMETRIC CONES

Self–scaled barrier functions are fundamental objects in the theory of interior–point methods for linear optimization over symmetric cones, of which linear and semidefinite programming are special cases. We are classifying all self–scaled barriers over irreducible symmetric cones and show that these functions are merely homothetic transformations of the universal barrier function. Together with...

Self-Scaled Barrier Functions on Symmetric Cones and Their Classification

Self-scaled Barriers for Semidefinite Programming

We show a result that can be expressed in any of the following three equivalent ways: 1. All self-scaled barrier functionals for the cone + of symmetric positive semideenite matrices are homothetic transformation of the universal barrier functional. 2. All self-scaled barrier functionals for + can be expressed in the form X 7 ! ?c 1 ln det X + c 0 for some constants c 1 > 0; c 0 2 R. 3. All sel...

Constructing self-concordant barriers for convex cones

In this paper we develop a technique for constructing self-concordant barriers for convex cones. We start from a simple proof for a variant of standard result [1] on transformation of a ν-self-concordant barrier for a set into a self-concordant barrier for its conic hull with parameter (3.08 √ ν + 3.57)2. Further, we develop a convenient composition theorem for constructing barriers directly fo...