论文标题
一种有效的半植物牛顿 - 基于牛顿-AMG的不精确原始二算法，用于广义运输问题
An efficient semismooth Newton-AMG-based inexact primal-dual algorithm for generalized transport problems
论文作者
论文摘要
这项工作涉及解决大量最佳质量运输问题的有效优化方法。从适当的动力学系统的时间离散化，通过使用Lyapunov函数的工具来提出一种不精确的原始偶对算法，为函数残留和可行性违反了全局（超级）线性收敛速率。所提出的算法包含一个内部问题，具有强大的半齿性特性，并激发了牛顿半植物迭代的使用。通过探索问题本身的隐藏结构，将牛顿迭代产生的线性系统等效地转移到了图形拉普拉斯系统中，为此，提出了强大的代数多机方法，并通过著名的Xu-Zikikatanov身份进行了分析。最后，提供了数值实验来验证我们方法的效率。
This work is concerned with the efficient optimization method for solving a large class of optimal mass transport problems. An inexact primal-dual algorithm is presented from the time discretization of a proper dynamical system, and by using the tool of Lyapunov function, the global (super-)linear convergence rate is established for function residual and feasibility violation. The proposed algorithm contains an inner problem that possesses strong semismoothness property and motivates the use of the semismooth Newton iteration. By exploring the hidden structure of the problem itself, the linear system arising from the Newton iteration is transferred equivalently into a graph Laplacian system, for which a robust algebraic multigrid method is proposed and also analyzed via the famous Xu--Zikatanov identity. Finally, numerical experiments are provided to validate the efficiency of our method.
