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Symmetricity of the Solution of Semidefinite Program

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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.

Contact: kanno@is-mj.archi.kyoto-u.ac.jp