Formulae for the L0, L1 and L∞ norms

The lack of ‘closed form’ solutions for the general linear models resulting from minimising the L0, L1 and L∞ norms is remarked on. Linear and integer programming models for deriving the parameters are given. General solutions are derived for these models by means of Fourier-Motzkin elimination. This results in formulae which can be applied to any data set to obtain the values of the norms and resulting parameters. These formulae also demonstrate known structural results concerning these models as well as providing results for statistical analysis.