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

Abstract

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