CODEWITHSUNDEEP
pythonoptimizationcvxpy
pythonml
pythonml

Reputation: 23

Python CVXPY matrix variable with fixed elements

I'm trying to use CVXPY to minimize an objective function with a quadratic term A.T @ P @ A with constant matrix P and variable matrix A, both of size n x n. This problem is not convex, but I want only A[0][0] as the variable while every other elements in A is fixed with constant values. In this way, the problem should be convex.

How do I express this problem in CVXPY? Declaring A as a variable matrix will always lead to CVXPY throwing errors that this problem does not follow DCP rules. Is there a way to declare the n x n matrix A with only the first element A[0][0] as the variable and everything else in A is fixed?

Upvotes: 2

Views: 733

Answers (1)

thomaskeefe
thomaskeefe

Reputation: 2374

Yes, use cvxpy.bmat to construct A as a block matrix.

A_00 = cvxpy.Variable(1)
A = cvxpy.bmat([[A_00, ... rest of row 1],
                [row 2],
                ...,
                [last row]])

More info: https://www.cvxpy.org/tutorial/functions/index.html#vector-matrix-functions

Upvotes: 1

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