How to force zero or positive entries in matrix when solving LMI?

Hi,

Using MATLAB's LMI tool (feasp), is there a way to force the solver to use only zero or positive entries in a matrix (decision variable). To be clear, I'm not asking about positive definiteness of the matrix, but about the entries of the matrix.

Sincerely, Rasmus

Answer 1

[Aquatris]

You can simply add another constraint to the LMI to impose the constraint.

For instance, assume decision variables are x and y. You are trying to solve;

   [10*x^2 -y+2*x ; 6*x y^2] > 0

and you want the -y+2*x to be positive. Then you can add another LMI term

    -y + 2*x > 0

or if you want them to be equal to 0, then

    -y + 2*x > 0
    -y + 2*x < 0