Thank you! I haven't yet been able to look at all of these resources. But at risk of sounding pedantic, in the resources that I am seeing, they are not using Lorentz cone set membership expressions. Rather, they created expressions like $x_3^2-(x_1-a)(x_2-b)\leq 0$.
Yes, they talked about these as conic forms, but that's not the same as saying that $(x_1-a,x_2-a,x_3)$ lie in some sort of cone. In fact, not all conic forms are convex! It's a slightly different context.
So this is actually important, because what it tells me, really, is that it might be better or at least easier to express these constraints using the
geo_mean function. And I'm pretty sure that if you do, you'll be able to use a single
geo_mean-based constraint to handle an entire swath of your individual constraints.
Regardless, this is extremely cool. I'm always thrilled to see applications of convex optimization in fields that I am unfamiliar with.