659 A New Primal-Dual Interior-Dual Interior-Point Method for Semidefinite Programming F. Alizadeh, J.P. Haeberly, M. Overton Semidefinite programming (SDP) is a convex optimization problem in the space of symmetric matrices. Primal-dual interiorpoint methods for SDP are discussed. These generate primal and dual matrices X and Z which commute only in the limit. A new method is proposed which iterates in the space of commuting matrices.