A split Levenberg-Marquardt method for large-scale sparse problems
针对每个残差只依赖少量变量的大规模稀疏非线性最小二乘问题，提出一种将原问题分裂为一系列独立小问题的Levenberg-Marquardt变体，降低了计算成本，并证明了全局收敛性和局部线性收敛性。
Abstract 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.