A curvilinear regression model is treated by linear programming methods, so as to require only mild restrictions on the nature of the non-linearities. Specifically a method is proposed that does not require assuming specific mathematical forms for the regression functions. Restrictive assumptions no stronger than monotonicity or concavity of the forms need be imposed. The linear programming formulations provide fits for the regression functions according to the criteria of minimal sum of absolute deviations and minimal maximum deviation. The alteration needed to employ a least squares fit is also sketched.