Year: 2018
Author: Cheng Chen, Zaiwen Wen, Yaxiang Yuan
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 6 : pp. 881–902
Abstract
A new two-level subspace method is proposed for solving the general unconstrained minimization formulations discretized from infinite-dimensional optimization problems. At each iteration, the algorithm executes either a direct step on the current level or a coarse subspace correction step. In the coarse subspace correction step, we augment the traditional coarse grid space by a two-dimensional subspace spanned by the coordinate direction and the gradient direction at the current point. Global convergence is proved and convergence rate is studied under some mild conditions on the discretized functions. Preliminary numerical experiments on a few variational problems show that our two-level subspace method is promising.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1706-m2016-0721
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 6 : pp. 881–902
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Nonlinear optimization Convex and nonconvex problems Subspace technique Multigrid/multilevel method Large-scale problems.