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A GENERAL TWO-LEVEL subspace METHOD FOR NONLINEAR OPTIMIZATION

Journal of Computational Mathematics 2018年第6期36卷 881-902页

作者： Cheng Chen Zaiwen Wen Yaxiang Yuan University of Chinese Academy of Sciences Beijing 100190 China LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Beijing International Center for Mathematical Research Peking University Beijing 100871 China LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

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

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subspace Minimization Conjugate Gradient Method Based on Cubic Regularization Model for Unconstrained Optimization

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Journal of Harbin Institute of Technology(New Series) 2021年第5期28卷 61-69页

作者： Ting Zhao Hongwei Liu School of Mathematics and Statistics Xidian UniversityXi'an 710126China

Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very *** the increasing emergence of large⁃scale problems,the subspace technology has become particularly important and widely used in the field of *** this study,a new CG method was put forward,which combined subspace technology and a cubic regularization ***,a special scaled norm in a cubic regularization model was *** certain conditions,some significant characteristics of the search direction were given and the convergence of the algorithm was *** comparisons show that for the 145 test functions under the CUTEr library,the proposed method is better than two classical CG methods and two new subspaces conjugate gradient methods.

关键词： cubic regularization model conjugate gradient method subspace technique unconstrained optimization

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