Iteratively regularized Gauss–Newton method for bound-constraint problems in atmospheric remote sensing Original Research Article

In this paper two algorithms for the solution of nonlinear ill-posed problems with simple bounds on the variables are presented. The proposed algorithms are bound-constraint versions of the iteratively regularized Gauss–Newton method. The numerical performances of the algorithms are studied by means of simulations concerning the retrieval of molecular concentrations from limb sounding observations. For these examples, the unconstrained algorithm leads to unreasonable solutions.