Linear systems in Jordan algebras and primal-dual interior-point algorithms


Recently F.Alizadeh, J.-P. Haeberly and M.Overton suggested a primal-dual interior-point algorithm for solving semidefinite problems that shows extremely good convergence properties and a high degree of accuracy.In the present paper we discuss a possibility of the extension of this algorithm for problems involving self-dual homogeneous cones. The question of solvability of a linear system arising in this algorithm is discussed. A nondeneracy theory for this class of problems is developed.

Technical Report, University of Notre Dame August, 1996