[Python] Recommended machine learning or deep learning algorithms to solve for Ax=b with...

Inputs:

A matrix A of size (m, n), where each row represents a linear equation, and each column represents a variable.

A vector x of size (n, 1), where some entries are known (i.e., provided values) and others are unknown (represented by NaN or None).

Objective:

The goal is to optimize the unknown values in x such that when b = A * x is computed, each element of b lies in the range (1.0, 1.20), i.e., for every entry b_i in vector b, the constraint 1.0 ≤ b_i ≤ 1.25 must hold. The values of x must be non zero.

Output:

An optimized vector x where the unknown entries have been determined such that the resulting b vector satisfies the given constraints.

I can't seem to converge to the solutions easily using optimization algorithm from CVXPY. Relaxing the constraints sometimes may or may not solve the problem! Is there any deep learning or machine learning approach that I could use to solve it? In future, I might wany to grow the vector x.

Here is a link to my coding. Error while running constraints optimization using cvxpy

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