Constraints of an L-shaped feasible region

[Jimbrisky]

I am writing the constraints for the feasible region within the L-shaped feasible region. The diagram is at this http://www.mathworks.com/help/optim/ug/writing-constraints.html

Are these equations the right constraints:

–1 ≤ x ≤ 1 and 0 ≤ y ≤ 1

Thanks for the help.

 

[Mark44]

I am writing the constraints for the feasible region within the L-shaped feasible region. The diagram is at this http://www.mathworks.com/help/optim/ug/writing-constraints.html

Are these equations the right constraints:

–1 ≤ x ≤ 1 and 0 ≤ y ≤ 1

No. These inequalities give you the rectangle whose corners are at (-1, 1), (1, 1), (1, 0), and (-1, 0). To get the whole L-shaped region you also need these constraints: 0 ≤ x ≤ 1 and -1 ≤ y ≤ 0.

The diagram at the page you linked to says this (slightly changed to use your x, y notation):

A point is in the rectangle –1 ≤ x ≤ 1 and 0 ≤ y ≤ 1 OR a point is in the rectangle 0 ≤ x ≤ 1 and -1 ≤ y ≤ 0

 

[Jimbrisky]

@Mark44, based on your explanation can I write the constraints for the feasible region as the union of two sets, Rx∪Ry, where

Rx:={(x,y):−1≤x≤1,0≤y≤1}

Ry:={(x,y):0≤x≤1,−1≤y≤1}.

Thanks for the help.

 

[Mark44]

Yes, although I don't know why you call one set R_x and the other one R_y. Better names might be R₁ and R₂.