截断非光滑牛顿多网格方法用于块分离最小化问题
Truncated Nonsmooth Newton Multigrid Methods for Block-Separable Minimization Problems
AI总结：
本文提出了一种稳健高效的截断非光滑牛顿多网格方法，用于求解广泛存在的块分离凸最小化问题，并证明了在弱条件下方法的全局收敛性。
摘要：
截断非光滑牛顿多网格（TNNMG）方法是一种稳健且高效的求解方法，适用于广泛存在的块分离凸最小化问题，通常源于非线性非光滑偏微分方程的离散化。本文证明了在弱条件下，该方法在目标函数和局部近似子问题求解器方面均具有全局收敛性。同时，本文讨论了多种算法选择，以使算法能够针对许多特定问题进行定制。数值例子被有意省略，因为许多此类例子已在其他地方发表。
英文摘要：
The Truncated Nonsmooth Newton Multigrid (TNNMG) method is a robust and efficient solution method for a wide range of block-separable convex minimization problems, typically stemming from discretizations of nonlinear and nonsmooth partial differential equations. This paper proves global convergence of the method under weak conditions both on the objective functional, and on the local inexact subproblem solvers that are part of the method. It also discusses a range of algorithmic choices that allows to customize the algorithm for many specific problems. Numerical examples are deliberately omitted, because many such examples have already been published elsewhere.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
