Numerical solution of nonlinear least squares problems arising in the simulating of environment pollutants

The solution of nonlinear least squares problems, which occurs in the study of pollutants by X-ray spectroscopy is considered. Although the solution of this problem is possible by general minimization methods, it is appropriate to take into account the specifics of the problem and to use special methods. Moreover, this problem has a system of linear equality constraints, which makes it impossible to use unconstrained optimization methods. The formulation of most problems with constraints gives rise to saddle point systems. Such systems have got semidefinite (1,1) blocks. An augmented Lagrangian method has been used for improving conditionality of the (1,1) block. Our attention has been focused on the symmetric/skew-symmetric splitting preconditioner. Numerical results are given for the problems with small and large number of unknown parameters.