We consider best approximation problems in a nonlinear subset ℳ of Banach space functions (

I present and discuss some general ideas about iterative nonlinear output least-squares methods. The main result is that, if it is possible to do forward modeling on a physical problem in a way that permits the output (i.e., the predicted values of some physical parameter that could be measured) and the rst derivative of the same output with respect to the model parameters (whatever they may be...