Help with some optimization code for Block Matrices

[Kaushal821]

TL;DR

Actually I am trying to generate a code for positive semidefinite programming, I have a block symmetric matrix of 256 elements (16x16) and I want to solve an equation using this, which looks like A - tX >=0 where A is known, t is a scalar variable and X is diagonal block matrix variable. So Ideally I have to optimize both t and X.

For this problem I am using 'cvxpy' library and using a set of constraints to optimize the value of t and X.

 

[pbuk]

What is the function that you are trying to minimize?

Can you see how to adapt the example code at https://www.cvxpy.org/examples/basic/sdp.html for your problem?

.. optimize the value of t and X.

I am not sure I understand: isn't the choice of $t$ arbitrary (if we have a solution $(t', X)$ then isn't $(t, \frac{t'}{t} X)$ an equivalent solution for any $t \ne 0$?) so we may as well set it to 1?