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

2010/04/01 by Éric Cancès, Virginie Ehrlacher, Cances, Eric +3 · 1 citation
Decision Sciences · Mathematics · Physics and Astronomy · #FOS: Mathematics #Functional Analysis (math.FA) #Model Reduction and Neural Networks #Numerical methods in inverse problems #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.1004.0095

openalex publication_date 2010/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

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