How to Convert Quadratic Contraint to Linear

Question

I have this constraint in my model:

(X - Y) @ B >= 0

where B is a boolean vector variable, X and Y are variables vector that represent quantities

I'm working with CVXPY, so I have to keep linear expressions

How could I translate this constraint in a way that is linear?

Could someone help me please ?

Erwin Kalvelagen · Answer 1 · 2022-02-02T07:01:10.843

1

I am assuming that X>=0 and Y>=0. In that case, we can somewhat easily linearize XB=X*B and YB=Y*B.

   XB <= X
   XB <= B*999
   XB >= X-999*(1-B)
   0 <= XB <= 999

Here 999 is an upper bound on X. Similar for YB. Now just add:

   XB >= YB

edited Feb 02 '22 at 07:01

answered Feb 01 '22 at 23:47

Erwin Kalvelagen

Thanks for your help and your time!, one question, I should add the same constraints for YB too?, YB <= Y, YB <= B*999, etc? – Alexis Olivero Aimaretti Feb 02 '22 at 13:13
Yes, "*Similar for YB*" – Erwin Kalvelagen Feb 02 '22 at 14:42

1 Answers1