A GENERAL TWO-LEVEL SUBSPACE METHOD FOR NONLINEAR OPTIMIZATION  

作　　者：Cheng Chen Zaiwen Wen Yaxiang Yuan 

机构地区：[1]University of Chinese Academy of Sciences, Beijing 100190, China LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences Beijing, China [2]Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China [3]LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Journal of Computational Mathematics》2018年第6期881-902,共22页计算数学（英文）

摘　　要：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.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.

关 键 词：Nonlinear optimization Convex and nonconvex problems Subspace technique Multigrid/multilevel method Large-scale problems 

分 类 号：O153.4[理学—数学] TQ522.1[理学—基础数学]