NDLI: On the Convergence of Recursive Trust-Region Methods for Multiscale Nonlinear Optimization and Applications to Nonlinear Mechanics

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Krause, Rolf Gross, Christian
Copyright Year	2009
Abstract	We prove new convergence results for a class of multiscale trust-region algorithms originally introduced by Gratton, Sartenaer, and Toint in [SIAM J. Optim., 19 (2008), pp. 414444] to solve unconstrained minimization problems within the Euclidean space $\mathbb{R}^n$. We will state less restrictive assumptions on the objective function and on the iteratively computed trust-region corrections, which allow for proving first-order convergence. Moreover, we propose a novel projection approach for obtaining the initial coarse level iterates, which are needed within the nonlinear multiscale iteration. We show the efficiency and robustness of our approach by means of numerical examples from nonlinear continuum mechanics, where stored energy functions for materials of Ogden-type and for materials with visco-plastic behavior are minimized.
Starting Page	3044
Ending Page	3069
Page Count	26
File Format	PDF
ISSN	00361429
DOI	10.1137/08071819X
e-ISSN	10957170
Issue Number	4
Volume Number	47
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-09-04
Access Restriction	Subscribed
Subject Keyword	nonlinear elasticity nonlinear multilevel methods nonlinear programming Mathematical programming methods Nonconvex programming, global optimization convergence theory Nonlinear programming Nonlinear elliptic equations Multigrid methods; domain decomposition
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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