Matrix with both integer and non integer values

MIDCP
1

Hello everyone,

I have a matrix of lets say n variables. Very few of them have to be integer and equal between them. I am a bit stack because till now I have not used a matrix with mixed values, only full integers or no integers. Can this be done somehow with the integer keyword? Is there an elegant way to do it? I tried:
variable UVW(length(X),3); variable UVW(Ufirst,1) integer; variable UVW(Vfirst,2) integer; variable UVW(Wfirst,3) integer;

But of course I get the error: Duplicate variable name: UVW.

Any idea?

2

You could declare integer variables and separately declare continuous variables. Then concatenate all the variables into the matrix you want.

variables a b
variable c integer
M = [a c;c b]

You can also use other keywords when declaring variables, as discussed in The Basics — CVX Users' Guide .
Here’s a (stupid) illustration

cvx_begin
variable X(2,2) diagonal integer
variable Y(2,2) banded(1,1)
Z = X + Y
minimize(trace(Z))
Z == semidefinite(2)
cvx_end

3

Just concatenating them as you did ruins the order though. Lets make up a scenario. Suppose you have :

        cvx_begin
        variable x(10)

And we need the first and the fifth to be integer. Appending the two integer ones at the end means we somehow have to rearrange them. Creating a new matrix of indices might solve this, but it is definitively not that elegant. Any suggestion? I did not probably make the problem clear in the initial question.

4 
variable a(2) integer
variable b(8)
x = [a(1);b(1:3);a(2);b(4:8)]

I’ll leave any elegance refinement and index wizardry to you.

5

Just use equality constraints. Create new integer variables, and constraint them to be equal to the elements in the matrix you need to be integers.

1 Like
6

This sounds cleaner. Thanks Michael.