A General Two-Level Subspace Method for Nonlinear Optimization

A General Two-Level Subspace Method for Nonlinear Optimization

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.

Author Details

Cheng Chen

Zaiwen Wen

Yaxiang Yuan