Symmetry of the Solution of Semidefinite Program by using Primal-Dual Interior-Point Method

摘要

Symmetry of an optimal solution of Semi-Definite Program (SDP) 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. The optimization problem of symmetric trusses under eigenvalue constraints is shown to be formulated as a symmetric SDP. Numerical experiments illustrate convergence to strictly symmetric optimal solutions.