self-scaled barrier functions – Optimization Online

Self-scaled barriers for irreducible symmetric cones

Published: 2001/04/10

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 a decomposition … Read more

Self-scaled barrier functions on symmetric cones and their classification

Published: 2001/03/28

Osman Guler

Raphael Hauser

Convex Optimization, Linear, Cone and Semidefinite Programming decomposition, interior point methods, jordan algebras, self-scaled barrier functions, symmetric cones, universal barrier function

Self-scaled barrier functions on self-scaled cones were introduced through a set of axioms in 1994 by Y.E. Nesterov and M.J. Todd as a tool for the construction of long-step interior point algorithms. This paper provides firm foundation for these objects by exhibiting their symmetry properties, their intimate ties with the symmetry groups of their domains … Read more