Understanding optimization at this level and being able to formulate your own problems in one of the canonical forms gives you super powers.
You don’t even have to build your own solvers. The commercial/open source ones are typically good enough.
But as a maintainer of solvespace (Open Source CAD software with geometric/algebraic constraint system) I am left wondering if this can be applied to our constraint solver, which I didn't write. It solves systems of algebraic constraints using some form of Newtons method, partial derivatives, jacobian... All stuff I'm familiar with, but not in great detail. Figuring out how best (and weather) to apply this might be a major digression ;-)
The interesting part (to me, as that is not my specialty) lies in the translation of the 3D constraints (including rotation, etc.) into a single objective function for solving Newton-style.
That's funny - I like the geometry stuff and have a good grasp of how to create useful constraint equations. I just don't know too much about the code for solving systems of those equations ;-)
For orientation we use quaternions. For other things it's an axis-angle representation. For the equal angle constraint I'm not sure how that's implemented. There was a recent addition of length-ratio between lines and arcs. That implementation was surprising to me.