How to set the sum of the absolute value of variables as inequality matrix and vector in linear programming?

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I am trying to solve a linear program with command "linprog". The inequality constrains has a sum of varaibles. e.g. I have 3 variable. x1,x2,x3.
The constrain should be like "abs(x1)+abs(x2)+abs(x3)<=2";
How to set this constrains in matlab?
I had read the link of two variables problem. But I can't figure out the rule of it. I can't derive the 3 case from it, either. Could anyone give me some suggestions? That will be very appreciated.

Accepted Answer

Bruno Luong
Bruno Luong on 18 Aug 2020
You can intruduce slack variables y1, y2, y3
x1 <= y1 and x1 >= -y1
x2 <= y2 and x2 >= -y2
x3 <= y3 and x3 >= -y3
y1+y2+y3 <= 2
Formulate your LP with
X:=[x1,x2,x3,y1,y2,y3]'
and the above constraints

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