Formally explain solver failures arising from mixed smooth vs. linear constraints

Establish a rigorous proof that the observed failures of generic convex solvers on levered AMM scenarios arise from the mixed smooth-versus-piecewise-linear constraint structure, which leads to interior versus corner solutions in the optimization landscape.

Background

The authors argue that markets with levered curves create piecewise-smooth constraints that sometimes behave like smooth problems and sometimes like linear programs, making standard convex solvers unreliable. They relate this to the difference between interior solutions (smooth) and corner solutions (linear), invoking a geometric analogy (the radome problem) later in the paper.

They state this relationship as a hypothesis and note they have not formally proved it.