Using a spectral scaling structured BFGS method for constrained nonlinear least squares

In this paper, we use a spectral scaled structured BFGS formula for approximating projected Hessian matrices in an exact penalty approach for solving constrained nonlinear least-squares problems. We show this spectral scaling formula has a good self-correcting property. The reported numerical results show that the use of the spectral scaling structured BFGS method outperforms the standard structured BFGS method.