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.

 

[CellCoree]

I would like to clarify that the constraints provided are not sufficient to define the L-shaped feasible region. The constraints should also consider the intersection point of the two lines in the L-shape, as well as any other relevant boundaries or conditions that may affect the feasibility of the region. Additionally, the constraints should be written in a way that clearly defines the boundaries of the region and allows for proper optimization and analysis. It is important to carefully consider all factors and variables when defining constraints in order to accurately represent the L-shaped feasible region.