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Automated Market Makers (AMMs) are decentralized applications that allow users to exchange crypto-tokens without the need for a matching exchange order. AMMs are one of the most successful DeFi use cases: indeed, major AMM platforms process…

Automated market makers (AMMs) are a new prototype of decentralised exchanges which are revolutionising market interactions. The majority of AMMs are constant product markets (CPMs) where exchange rates are set by a trading function. This…

In this paper, a decentralized proximal method of multipliers (DPMM) is proposed to solve constrained convex optimization problems over multi-agent networks, where the local objective of each agent is a general closed convex function, and…

The role of a market maker is to simultaneously offer to buy and sell quantities of goods, often a financial asset such as a share, at specified prices. An automated market maker (AMM) is a mechanism that offers to trade according to some…

Submodular functions, as well as the sub-class of decomposable submodular functions, and their optimization appear in a wide range of applications in machine learning, recommendation systems, and welfare maximization. However, optimization…

Constant function market makers(CFMMS) are a popular market design for decentralized exchanges(DEX). Liquidity providers(LPs) supply the CFMMs with assets to enable trades. In exchange for providing this liquidity, an LP receives a token…

Batch auctions are a classical market microstructure, acclaimed for their fairness properties, and have received renewed interest in the context of blockchain-based financial systems. Constant function market makers (CFMMs) are another…

Supply chain transportation operations often account for a large proportion of product total cost to market. Such operations can be optimized by solving the Logistics Service Network Design Problem (LSNDP), wherein a logistics service…

Decentralized exchanges (DEXs) form a cornerstone of the decentralized finance (DeFi) ecosystem, processing token trades worth billions of dollars daily. Yet, a significant fraction of these trades are suboptimal: alternative routing paths…

We study a network utility maximization (NUM) decomposition in which the set of flow rates is grouped by source-destination pairs. We develop theorems for both single-path and multipath cases, which relate an arbitrary NUM problem involving…

This paper develops a robust mathematical framework for Constant Function Market Makers (CFMMs) by transitioning from traditional token reserve analyses to a coordinate system defined by price and intrinsic liquidity. We establish a…

Automated market makers are a popular mechanism used on decentralized exchange, through which users trade assets with each other directly and automatically through a liquidity pool and a fixed pricing function. The liquidity provider…

We demonstrate the application of an algorithmic trading strategy based upon the recently developed dynamic mode decomposition (DMD) on portfolios of financial data. The method is capable of characterizing complex dynamical systems, in this…

Network function virtualization enables network operators to implement new services through a process called service function chain mapping. The concept of Service Function Chain (SFC) is introduced to provide complex services, which is an…

In the distributed optimization problem for a multi-agent system, each agent knows a local function and must find a minimizer of the sum of all agents' local functions by performing a combination of local gradient evaluations and…

Despite their high accuracy, complex neural networks demand significant computational resources, posing challenges for deployment on resource constrained devices such as mobile phones and embedded systems. Compression algorithms have been…

Automated Market Makers (AMMs) are used to provide liquidity for combinatorial prediction markets that would otherwise be too thinly traded. They offer both buy and sell prices for any of the doubly exponential many possible securities that…

A class of finite-state and discrete-time optimal control problems is introduced. The problems involve a large number of agents with independent dynamics, which interact through an aggregative term in the cost function. The problems are…

Solving large scale entropic optimal transport problems with the Sinkhorn algorithm remains challenging, and domain decomposition has been shown to be an efficient strategy for problems on large grids. Unbalanced optimal transport is a…

Automated Market Makers (AMMs) are major centers of matching liquidity supply and demand in Decentralized Finance. Their functioning relies primarily on the presence of liquidity providers (LPs) incentivized to invest their assets into a…