Necessary and sufficient conditions for global optimality of eigenvalue optimization problems |
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Authors: | Y Kanno M Ohsaki |
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Affiliation: | (1) Department of Architecture and Architectural Systems, Kyoto University, Sakyo, Kyoto 606-8501, Japan e-mail: kanno@is-mj.archi.kyoto-u.ac.jp, ohsaki@archi.kyoto-u.ac.jp, JP |
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Abstract: | The necessary and sufficient conditions for global optimality are derived for an eigenvalue optimization problem. We consider
the generalized eigenvalue problem where real symmetric matrices on both sides are linear functions of design variables. In
this case, a minimization problem with eigenvalue constraints can be formulated as Semi-Definite Programming (SDP). From the
Karush-Kuhn-Tucker conditions of SDP, the necessary and sufficient conditions are derived for arbitrary multiplicity of the
lowest eigenvalues for the case where important lower bound constraints are considered for the design variables.
Received May 18, 2000 |
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Keywords: | : eigenvalue optimization optimality condition semidefinite programming multiple eigenvalues generalized eigenvalue problem |
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