Some results on the \(\mathcal U\)-Langrangian of a class of maximum eigenvalue functions (Q2825528)
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scientific article; zbMATH DE number 6638358
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some results on the \(\mathcal U\)-Langrangian of a class of maximum eigenvalue functions |
scientific article; zbMATH DE number 6638358 |
Statements
13 October 2016
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nonsmooth optimization
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\(\mathcal U\)-Lagrangian
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maximum eigenvalue function
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\(\mathcal UV\)-space decomposition
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Some results on the \(\mathcal U\)-Langrangian of a class of maximum eigenvalue functions (English)
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The \(\mathcal UV\)-theory is the sum of two orthogonal subspaces \(\mathcal U\) and \(\mathcal V\) in such a way that all of nonsmoothness is concentrated in \(\mathcal V\) such that the first-order approximation of the maximum eigenvalue function is linear in \(\mathcal U\). This paper gives three kinds of \(\mathcal UV\)-space decomposition of a class of maximum eigenvalue functions and the proof about the equivalency of the three pair subspaces. The first-order and second-order approximations for a class of maximum eigenvalue functions are presented. The necessary and sufficient condition on the continuity of a set of minimizers of the \(\mathcal U\)-Langrange function is obtained.
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