How I can implement a non-overlap optimization constraint

I am doing a global optimiation process using matlab. I need to implement a non-overlap constraint to prevnt 2 rectangles from overlap each other. I wonder if any one has faced such constraint in matlab optimization

[Matt J]

How are the rectangles parametrized?

[Mohamed Salem]

Well, I optimize the location of 2 rectangles, but if it is possible to do more or having a generic constraint for (n) of them, it would be better

Answer 1

[Matt J]

If V1 (4x2) and V2(4x2) are the vertices of the two rectangles, then you could introduce additional unknowns a,b,c with the constraints,

V1*[a;b]>=c
V2*[a;b]<=c

[Mohamed Salem]

The optimization objective is to locate the both rectangles, what is a,b,and c ?

[Matt J]

They are additional unknown variables introduced to parametrize the non-overlap constraints. You need to solve for them along with your original unknowns.