Related papers: Optimal Routing across Constant Function Market Ma…

We consider the problem of optimally executing an order involving multiple crypto-assets, sometimes called tokens, on a network of multiple constant function market makers (CFMMs). When we ignore the fixed cost associated with executing an…

Optimization is widely used to determine the physical and financial exchange of wholesale electricity in organized markets. Guarantees of solution optimality and feasibility rest largely on convexity, which is not in general a…

Fuel cost contributes to a significant portion of operating cost in cargo transportation. Though classic routing models usually treat fuel cost as input data, fuel consumption heavily depends on the travel speed, which has led to the study…

We consider the problem of optimally executing a user trade over networks of constant function market makers (CFMMs) in the presence of hooks. Hooks, introduced in an upcoming version of Uniswap, are auxiliary smart contracts that allow for…

We suggest a framework to determine optimal trading fees for constant function market makers (CFMMs) in order to maximize liquidity provider returns. In a setting of multiple competing liquidity pools, we show that no race to the bottom…

The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…

Energy saving is becoming an important issue in the design and use of computer networks. In this work we propose a problem that considers the use of rate adaptation as the energy saving strategy in networks. The problem is modeled as an…

Constant function market makers (CFMMs) such as Uniswap have facilitated trillions of dollars of digital asset trades and have billions of dollars of liquidity. One natural question is how to optimally route trades across a network of CFMMs…

This paper studies an important rate allocation problem that arises in many networked and distributed systems: steady-state traffic rate allocation from multiple sources to multiple service nodes when both (i) the access-path delay on each…

We investigate approximately optimal mechanisms in settings where bidders' utility functions are non-linear; specifically, convex, with respect to payments (such settings arise, for instance, in procurement auctions for energy). We provide…

This work focuses on the mathematical study of constant function market makers. We rigorously establish the conditions for optimal trading under the assumption of a quasilinear, but not necessarily convex (or concave), trade function. This…

Constant Function Market Makers (CFMMs) are a tool for creating exchange markets, have been deployed effectively in prediction markets, and are now especially prominent in the Decentralized Finance ecosystem. We show that for any set of…

We introduce a new framework for optimal routing and arbitrage in AMM driven markets. This framework improves on the original best-practice convex optimization by restricting the search to the boundary of the optimal space. We can…

Automated market makers with concentrated liquidity capabilities are programmable at the tick level. The maximization of earned fees, plus depreciated reserves, is a convex optimization problem whose vector solution gives the best provision…

We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…

Stochastic matching is the stochastic version of the well-known matching problem, which consists in maximizing the rewards of a matching under a set of probability distributions associated with the nodes and edges. In most stochastic…

We extend in two ways the standard Karush-Kuhn-Tucker optimality conditions to problems with a convex objective, convex functional constraints, and the extra requirement that some of the variables must be integral. While the standard…

Gas transportation and storage has become one of the most relevant and important optimization problems in energy systems. This problem inherently includes highly nonlinear and nonconvex aspects due to gas physics, and discrete aspects due…

We formulate the optimal flow problem in a multi-area integrated electrical and gas system as a mixed-integer optimization problem by approximating the non-linear gas flows with piece-wise affine functions, thus resulting in a set of…

Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Given the non-convex nature of gas transmission constraints, global optimality and infeasibility…