A Randomised Subspace Gauss-Newton Method for Nonlinear Least-Squares. (arXiv:2211.05727v1 [math.OC])

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 …

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