Fitting a line by the method of least absolute deviations

2 Fitting a line by the method of least absolute deviations 

Me will discuss many times the problem of adjusting the parameters a and b of the linear function = ax + b in order to fit the line to the set 

This problem can be translated into one of linear programming. Introducing the variables s 0 we first construct an equivalent constrained minimization problem given by 

Thus both the constraints and the objective function are linear. 

The only remaining problem is that a and b are not necessarily nonnegative, as required in linear programming. Inventing further new variables al a2 bl t 2 0 and setting a = a - a2 and b = b - t 2 will eliminate 

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