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 is positive definite. Or equivalently

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

when you set

\begin{align*}
Q&=A^TA \\
q&=A^Tb
\end{align*}

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.

Link to the documentation.