Convergence of a greedy algorithm for high-dimensional convex nonlinear problems
Functional Analysis
2015-03-13 v2
Abstract
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.
Cite
@article{arxiv.1004.0095,
title = {Convergence of a greedy algorithm for high-dimensional convex nonlinear problems},
author = {Eric Cances and Virginie Ehrlacher and Tony Lelievre},
journal= {arXiv preprint arXiv:1004.0095},
year = {2015}
}
Comments
36 pages, 9 figures, accepted in Mathematical Models and Methods for Applied Sciences