I'm trying to follow this older paper, page 19.
The goal is to solve: $\min \|Ax-b\|^2 s.t. Gx \ge h$ given $A, G, b, h$
By combining the equations into a single LCP of the form: $Mz + q = w$ s.t. $z \ge 0, w \ge 0, z \perp w$
To do this, they form a single large equation: $f(r,w,x,y,z) = \frac{1}{2} r^Tr - y^T(r+Ax-b) - z^T(Gx-w-h)$
And take the partial derivatives with respect to each variable to construct a large system of equations and work from there. I'm fine with their math once the above equation is constructed, but I'm confused where some of the new variables come from.
$r = Ax - b$, so $r$ is just the residual vector that we want to minimize (ideally it's $0$), and they state that at the top of the section. Presumably $y$ and $z$ are something similar, but where they come from seems less clear to me.
I looked in earlier sections in the paper but I don't see anything that explains it.