MATLAB: Linprog optimisation with slack variable. How to formulate the matices

linprogMATLABoptimisationslack variable

I am trying to do a basic linear fitting optimisation, but am not getting the results that I am expecting. I have generated data for x and y – x=linspace(0,1,50) and y = 4x-1. And need to use a slack variable.
My optimisation problem then becomes
    min(a,b,s) s subject to -s <= a*x(i)+b-y(i) <= s
The code I am using to try and get a = 4 and b= -1 is:
    %    a  b  s
    f = [0 ;0 ;1];
    A1 = [ J ones(N,1)];
    A2 = [-J ones(N,1)];
    A = [A1 ;A2]; 
    b1 = y;
    b2 = -y;
    b  = [b1 ;b2];
    [a b s] = linprog(f,A,b);
J has been defined as [x ones(50,1)]
Can anybody help me please?
Thanks in advance.

Best Answer

A1 = [x,ones(N,1),-ones(N,1)];
A2 = [-x,-ones(N,1),-ones(N,1)];
A = [A1;A2];
b = [y;-y];
f = [0;0;1];
linprog(f,A,b)
Best wishes
Torsten.
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