Convergence of a greedy algorithm for high-dimensional convex nonlinear problems (Q2892231)
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scientific article; zbMATH DE number 6047347
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convergence of a greedy algorithm for high-dimensional convex nonlinear problems |
scientific article; zbMATH DE number 6047347 |
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18 June 2012
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convex optimization
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greedy algorithm
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obstacle problem
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uncertainty quantification
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tensor product decomposition
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Hilbert space
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convergence
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numerical results
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Convergence of a greedy algorithm for high-dimensional convex nonlinear problems (English)
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This paper presents a new algorithm to compute the global minimum of a strongly convex energy functional. For this purpose the authors propose a tensor product decomposition of the considered space into two Hilbert spaces to formulate then a greedy algorithm based on this decomposition. The convergence of the method is shown provided that the gradient of the energy is Lipschitz on bounded sets. Furthermore, in the finite-dimensional case, a fast rate on convergence is shown. The extension of the results for a splitting into more than two Hilbert spaces is discussed. Numerical results illustrate the behavior of the proposed method using a one-dimensional membrane problem with uncertainty.
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