Necessary and sufficient conditions for global optimality of eigenvalue optimization problems

Necessary and sufficient conditions for global optimality of eigenvalue optimization problems

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Article ID: iaor2014903
Volume: 22
Issue: 3
Start Page Number: 248
End Page Number: 252
Publication Date: Oct 2001
Journal: Structural and Multidisciplinary Optimization
Authors: ,
Keywords: matrices
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.

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