论文标题
分裂的Levenberg-Marquardt方法用于大规模稀疏问题
Splitted Levenberg-Marquardt Method for Large-Scale Sparse Problems
论文作者
论文摘要
我们考虑大规模的非线性最小二乘正方形问题的稀疏残差问题，每个方块都取决于少量变量。提出和分析了将原始问题分解为一系列独立问题的序列的去耦过程。较小的大小问题的修改方式可以抵消忽略依赖依赖的错误，从而使我们能够拆分原始问题。最终的方法是对Levenberg-Marquardt方法的修改，其计算成本较小。在适当的稀疏性假设下，全球收敛既证明是局部线性收敛的。该方法在网络定位模拟问题上进行了测试，其中最多100万个变量，并证明了该方法的效率。
We consider large-scale nonlinear least squares problems with sparse residuals, each of them depending on a small number of variables. A decoupling procedure which results in a splitting of the original problems into a sequence of independent problems of smaller sizes is proposed and analysed. The smaller size problems are modified in a way that offsets the error made by disregarding dependencies that allow us to split the original problem. The resulting method is a modification of the Levenberg-Marquardt method with smaller computational costs. Global convergence is proved as well as local linear convergence under suitable assumptions on sparsity. The method is tested on the network localization simulated problems with up to one million variables and its efficiency is demonstrated.
