Necessary and sufficient conditions for global optimality of eigenvalue optimization problems

被引：0
|
作者：
Y. Kanno
M. Ohsaki
机构：
[1] Department of Architecture and Architectural Systems,
[2] Kyoto University,undefined
[3] Sakyo,undefined
[4] Kyoto 606-8501,undefined
[5] Japan e-mail: kanno@is-mj.archi.kyoto-u.ac.jp,undefined
[6] ohsaki@archi.kyoto-u.ac.jp,undefined
来源：
Structural and Multidisciplinary Optimization | 2001年 / 22卷
关键词：
Key words: eigenvalue optimization, optimality condition, semidefinite programming, multiple eigenvalues, generalized eigenvalue problem;
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摘要：
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.
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页码：248 / 252
页数：4
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