"Traditional arbitrage methods relying on convex optimization struggle in AMM-driven markets because they assume smooth constraints that rarely exist in practice. As detailed in the paper, convex formulations, while effective for canonical xy=k curves, fall short when applied to concentrated liquidity AMMs.

In these settings, the optimization problem involves piecewise-linear constraints, where solutions frequently lie at the boundary of the feasible region. This mismatch forces solvers into convergence challenges, as gradient-based methods fail near abrupt transitions and simplex methods jump between vertices. The result is a system that, despite its mathematical elegance, is slow, unpredictable, and ill-suited for real-time arbitrage where every millisecond counts."