Question

how to do you get the constraints for an L-shaped feasible region like the one in the attached image

Answer 1

One way to do it is a sort of case-by-case approach.

The desired region is a subset of the region given by
\[R:=\{(x,y)~:~-1\le x\le1,~-1\le y\le1\}\]
You can write this subset as the union of two sets, \(R_x\cup R_y\), where
\[R_{x}:=\{(x,y)~:~-1\le x\le1,~0\le y\le1\}\\
R_{y}:=\{(x,y)~:~0\le x\le1,~-1\le y\le1\}\]
Another way to do is a subset of three square regions \(R_1\cup R_2\cup R_3\), with
\[R_1:=\{(x,y)~:~-1\le x\le1,~0\le y\le1\}\\
R_2:=\{(x,y)~:~0\le x\le1,~0\le y\le1\}\\
R_3:=\{(x,y)~:~0\le x\le1,~-1\le y\le0\}\]

Answer 2

There may be a more explicit way to write it using step functions...

Answer 3

Ok. I will try to think of that. Thanks

Answer 4

yw