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Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2011

Convergence of a greedy algorithm for high-dimensional convex nonlinear problems

Résumé

In this article, we present a greedy algorithm based on a tensor product decomposition, whose aim is to compute the global minimum of a strongly convex energy functional. We prove the convergence of our method provided that the gradient of the energy is Lipschitz on bounded sets. The main interest of this method is that it can be used for high-dimensional nonlinear convex problems. We illustrate this method on a prototypical example for uncertainty propagation on the obstacle problem.

Dates et versions

hal-00469622 , version 1 (02-04-2010)

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Eric Cancès, Virginie Ehrlacher, Tony Lelièvre. Convergence of a greedy algorithm for high-dimensional convex nonlinear problems. Mathematical Models and Methods in Applied Sciences, 2011, 21 (12), pp.2433-2467. ⟨10.1142/S0218202511005799⟩. ⟨hal-00469622⟩
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