jaxnnls 1.0.0

The jaxnnls package provides functions to solve non-negative

JaxNNLS

This package can be used for solving non-negative least square (NNLS) problems of the following form:

$$ \begin{align*} \underset{x}{\text{minimize}} & \quad \frac{1}{2}x^TQx - q^Tx \ \text{subject to} & \quad x \geq 0 \end{align*} $$

where $Q \succeq 0$. Or equivalently

$$ \begin{align*} \underset{x}{{\text{solve}}} & \quad Ax = b \ \text{subject to} & \quad x \geq 0 \end{align*} $$

where $A^TA = Q$ and $A^Tb = q$.

This solver can be combined with JAX's jit and vmap functionality, as well as differentiated with reverse-mode grad.

The NNLS problem is solved with a primal-dual interior point algorithm. This code is a modification on the qpax package, but in the special case of NNLS. Because of the simplifications in this special case the resulting code is significantly faster when $Q$ large in size.

As with the qpax code, derivative smoothing can be applied to the gradients.