Robust solutions to a general class of approximation problems

The solution of robust counterparts of optimization problems with uncertain data is currently attracting much interest. In particular, this has been considered in the context of approximation using total least squares. Here we consider the analogue of this in the errors-invariables context, where attention is focused on the particular errors which arise in the individual independent variable values in data fitting problems. In addition to consideration of problems which are linear in the free parameters, some suggestions are made for the treatment of nonlinear problems. The emphasis throughout is on providing methods which are computationally tractable, and the results parallel and extend earlier results on uncertain linear approximation problems.