| Symmetricity Of The Solution Of Semidefinite Program (2007) | |||||||||||||||||
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| . Symmetricity of an optimal solution of SemiDefinite Program (SDP) with certain symmetricity is discussed based on symmetry property of the central path that is traced by a primaldual interior-point method. Introducing some operators for rearranging elements of matrices and vectors, three types of symmetric SDPs are defined by using those operators. The symmetricity of the solution on the central path is proved for each of symmetric SDPs. Therefore, it is theoretically guaranteed that a symmetric optimal solution is always obtained by using a primal-dual interiorpoint method even if there are other asymmetric optimal solutions. As an application of this result, we consider topology optimization problems of symmetric trusses that belong to one of the three types of symmetric SDPs, and we shall show that the symmetric optimal solution can be found regardless of the choice of member numbering and coordinate systems. Numerical experiments by using several algorithms for SDP illustrate rap... | |||||||||||||||||
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