Python Help with some optimization code for Block Matrices

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The discussion centers on using the 'cvxpy' library for optimization, specifically focusing on minimizing a function involving variables t and X under certain constraints. A key point raised is the potential arbitrariness of the variable t; it is suggested that if a solution exists for (t', X), then scaling X by t' and setting t to 1 could yield an equivalent solution. This raises questions about the necessity of optimizing t when it may not impact the overall solution. The conversation also references adapting example code from the cvxpy documentation to fit the specific optimization problem at hand.
Kaushal821
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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.
 
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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?

Kaushal821 said:
.. 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?
 
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