论文标题
非线性最小二乘的随机子空间高斯牛顿法
A Randomised Subspace Gauss-Newton Method for Nonlinear Least-Squares
论文作者
论文摘要
我们提出了一种随机子空间高斯 - 纽顿（R-SGN）算法，用于求解非线性最小二乘优化问题，该算法使用可变域中的残留物的草图jacobian，并在每种迭代中求解了降低的最小值线性。为R-SGN的信任区域变体提供了均匀的全局收敛结果，具有很高的概率，与确定性对应物相匹配的结果可以取决于准确性公差的顺序。对于逻辑回归和最可爱的收集的非线性回归问题，提出了有希望的初步数值结果。
We propose a Randomised Subspace Gauss-Newton (R-SGN) algorithm for solving nonlinear least-squares optimization problems, that uses a sketched Jacobian of the residual in the variable domain and solves a reduced linear least-squares on each iteration. A sublinear global rate of convergence result is presented for a trust-region variant of R-SGN, with high probability, which matches deterministic counterpart results in the order of the accuracy tolerance. Promising preliminary numerical results are presented for R-SGN on logistic regression and on nonlinear regression problems from the CUTEst collection.
