Uniswap—and other constant product markets—appear to work well in practice despite their
simplicity. In this paper, we give a simple formal analysis of constant product markets and …

We introduce MathOptInterface, an abstract data structure for representing mathematical
optimization problems based on combining predefined functions and sets. MathOptInterface …

Many convex optimization problems can be represented through conic extended
formulations (EFs) using only the small number of standard cones recognized by advanced …

We present GPkit, a Python toolkit for Geometric and Signomial Programming that prioritizes
explainability and incremental complexity. GPkit was designed through an ethnographic …

We describe a generalization of the Sums-of-AM/GM-Exponential (SAGE) methodology for
relative entropy relaxations of constrained signomial and polynomial optimization problems …

Robust Markov decision processes (MDPs) are used for applications of dynamic
optimization in uncertain environments and have been studied extensively. Many of the …

In recent work, we provide computational arguments for expanding the class of proper cones
recognized by conic optimization solvers, to permit simpler, smaller, more natural conic …

Convex programming plays a fundamental role in machine learning, data science, and
engineering. Testing convexity structure in nonlinear programs relies on verifying the …

Modern modeling languages for general physical systems, such as Modelica, Amesim, or
Simscape, rely on Differential Algebraic Equations (DAEs), ie, constraints of the form f (x …

Using the dual cone of sums of nonnegative circuits (SONC), we provide a relaxation of the
global optimization problem to minimize an exponential sum and, as a special case, a …