Re: constraint on non-square matrix

[Johan Löfberg]

It is very unclear what you are asking.

You talk about a  biliinear products x1'*C12*x2 which is a scalar. You want this to be negative(?). Why is it a problem that C12 is non-square? It has to be, otherwise the product x1*C12*x2   cannot be constructed uinless d1=d2

torsdag 20 maj 2021 kl. 18:16:01 UTC+2 skrev Ash:

I have a n-dimensional decision variable "x" that has two components "x1" (dimension "d1) and "x2" (dimension "d2") such that "d1 + d2 = n". 

I also have a (n x n)-correlation matrix between variables (x1, x2): C = [C1 C12;C12' C2] with C1 being "d1 x d1", C12 being "d1 x d2", and C2 being "d2 x d2". 

I am trying to enforce a constraint such that the optimizer can attempt to figure out "x2" that minimize correlation to "x1" which already has constraints on. I was thinking to enforce "x1'*C12*x2 <= 0" but C12 is non-square. Is there another way to achieve this? For example, by zeroing out the block matrices C1, C2 (with diagonals 1) and enforce "x'*C*x <= 0" with C being PD?