  We present DFO-GN, a derivative-free version of the Gauss-Newton method for
solving nonlinear least-squares problems. As is common in derivative-free
optimization, DFO-GN uses interpolation of function values to build a model of
the objective, which is then used within a trust-region framework to give a
globally-convergent algorithm requiring $O(\epsilon^{-2})$ iterations to reach
approximate first-order criticality within tolerance $\epsilon$. This algorithm
is a simplification of the method from [H. Zhang, A. R. Conn, and K.
Scheinberg, A Derivative-Free Algorithm for Least-Squares Minimization, SIAM J.
Optim., 20 (2010), pp. 3555-3576], where we replace quadratic models for each
residual with linear models. We demonstrate that DFO-GN performs comparably to
the method of Zhang et al. in terms of objective evaluations, as well as having
a substantially faster runtime and improved scalability.
