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Resolve convergence issues of the Angeris et al. convex optimization on levered AMMs

Investigate and resolve the convergence issues encountered when applying the Angeris et al. (2021) convex optimization formulation for AMM arbitrage to levered (concentrated-liquidity) constant-product AMMs, clarifying whether and how that convex approach can be made to converge in such settings.

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Background

The paper began with the standard convex optimization approach for AMM arbitrage from Angeris et al. (2021). While this method worked on unlevered curves, the authors report persistent convergence failures when levered (concentrated) curves are present, which motivated the development of their marginal price method.

Understanding and fixing these convergence issues would determine whether the widely used convex formulation can be reliably deployed in markets containing concentrated liquidity or whether alternative formulations are necessary.

References

This approach worked very well on unlevered curves, but as soon as we applied it to levered curves, we ran into convergence issues that we could not ultimately solve.

Marginal Price Optimization (2502.08258 - Loesch et al., 12 Feb 2025) in Section 1, Introduction (footnote)