Mathematical Programming Computation, Volume 11, Issue 4, December 2019
A derivative-free Gauss–Newton method
Coralia Cartis, Lindon Roberts
We present DFO-GN, a derivative-free version of the Gauss–Newton method for solving nonlinear least-squares problems.
DFO-GN uses linear
interpolation of residual values to build a quadratic model of the
objective, which is then used within a typical derivative-free trust-region framework. We show that DFO-GN is globally
convergent and requires at most O(??2) iterations to reach approximate first-order criticality within tolerance ?.
We provide an implementation of DFO-GN and compare it to other state-of-the-art derivative-free solvers that use quadratic
interpolation models. We demonstrate numerically that despite using only linear residual models, DFO-GN performs
comparably to these methods in terms of objective evaluations. Furthermore, as a result of the simplified interpolation
procedure, DFO-GN has superior runtime and scalability. Our implementation of DFO-GN is available at
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