Back to Nonlinear Least Squares

The algorithms in the VE10 and LANCELOT packages address nonlinear least squares problems where \(f^\prime(x)\) is large and sparse. The algorithms make use of the assumption that each \(f_i\) is a partially separable function to compute compact quasi-Newton approximations to the Hessian matrices \(\nabla^2 f_i\). At each iteration, a choice is made between a Gauss-Newton step and a step derived from a structured quasi-Newton Hessian approximation. The step is obtained by applying a conjugate gradient method to one of these model choices.