Symmetricity of the Solution of Semidefinite Program

Y. Kanno, M. Ohsaki and N. Katoh

Symmetricity of an optimal solution of Semi-Definite Program (SDP) with certain symmetricity is discussed based on symmetry property of the central path that is traced by a primal-dual interior-point method. A symmetric SDP is defined by operators for rearranging elements of matrices and vectors, and the solution on the central path is proved to be symmetric. Therefore, it is theoretically guaranteed that a symmetric optimal solution is always obtained by using a primal-dual interior-point method even if there exist other asymmetric optimal solutions. The optimization problem of symmetric trusses under eigenvalue constraints is shown to be formulated as a symmetric SDP. Numerical experiments by using an interior-point algorithm illustrate convergence to strictly symmetric optimal solutions.

AIS Reserch Report 00-01, Architectural Information Systems Laboratory, Kyoto University, Sakyo, Kyoto 606-8501, Japan, July, 2000.