In this paper linear control-approximation problems in normed spaces are considered. The control-approximation problems are transformed into several “fit” optimizaion problems by the aid of the Fenchell-Rockafellar duality theorem. Hitherto in the literature such optimization problems have been constructed in a different way. The duality theorem of Fenchel-Rockafellar enables a completely uniform treatment and provides known propositions and also new results.