python solve the simultaneous equations with solutions > 0

Question

I have simultaneous equations(with many equations), which are no solution, and I need to find a best solutions. Each element of solution must>0 (no 0 or negative).

np.linalg.lstsq could get the best solution, but may also appear negative elements.

scipy.optimize.nnls could get best solution without negative elements, but may also appear 0.

How can I restrict to get the best solution with each element>0 or is there any other function can use to solve the problem?

Answer 1

For each parameter p , define p_ = p - eps for very small eps .

Solve for {p_} , then assign p = p_ + eps and you get all parameters above zero.

In practice, just add epsilon to the solution.

If that doesn't suffice, please explain why.