\(\mathcal{UV}\)-theory of a class of semidefinite programming and its applications (Q2240656)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(\mathcal{UV}\)-theory of a class of semidefinite programming and its applications |
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\(\mathcal{UV}\)-theory of a class of semidefinite programming and its applications (English)
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4 November 2021
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Convex semidefinite optimization problems are converted into eigenvalue problems by means of exact penalty functions. First-and second-order derivatives of the \(\mathcal{U}\)-Lagrangian of the function of the largest eigenvalues are derived under a transversality condition holds. A conceptual algorithm with superlinear convergence for \(\mathcal{UV}\)-decomposition is proposed, and an application involving an opimization problem containing a bilinear matrix inequality in the constraints is studied.
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semidefinite programming
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nonsmooth optimization
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eigenvalue optimization
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\(\mathcal{UV}\)-decomposition
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\(\mathcal{U}\)-Lagrangian
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smooth manifold
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second-order derivative
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