Jordan algebraic approach to symmetric optimization

Jordan algebraic approach to symmetric optimization

Vieira, M.V.C.

Roos, C. (promotor)

Electrical Engineering, Mathematics and Computer Science

2007-11-13

In this thesis we present a generalization of interior-point methods for linear optimization based on kernel functions to symmetric optimization. It covers the three standard cases of conic optimization: linear optimization, second-order cone optimization and semi-definite optimization. We give an introduction to Euclidean Jordan algebras and explain the connection between such algebras and symmetric cones. We establish some properties of eigenvalues in Jordan algebras and prove that the barrier functions based on kernel functions are separable spectral functions that only depend on the eigenvalues of their arguments. We propose an interior-point algorithm for symmetric optimization and derive its complexity bound.

interior-point methods
symmetric cones
Kernel functions
Jordan algebras

http://resolver.tudelft.nl/uuid:6a2cad07-86c3-4a16-9d04-1224ef4d900f

978-90-6464-1893

Institutional Repository

doctoral thesis

(c) 2007 M.V.C. Vieira