  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.
