Robust counterparts of errors-in-variables problems

Of interest here are linear data fitting problems with uncertain data which lie in a given uncertainty set. A robust counterpart of such a problem may be interpreted as the problem of finding a solution which is best over all possible perturbations of the data which lie in the set. In particular, robust counterparts of total least squares problems have been studied and good algorithms are available. The purpose of this paper is to consider robust counterparts of the problems considered as errors-in-variables problems, when it is appropriate to work directly with the uncertain variable values. It is shown how the original problems can be replaced by convex optimization problems in fewer variables for which standard software may be applied.