JuliaCon 2026

This talk introduces AlgorithmAnalysis.jl, a Julia package that automates the worst-case analysis of black-box algorithms. Analyzing the performance of an algorithm by hand is both tedious and error prone. This package enables users to express algorithms in a natural way using a high-level domain-specific language. This symbolic description is then transformed behind the scenes into a semidefinite program that is solved numerically to construct tight numerical bounds on the worst-case performance. The package implements the performance estimation problem (PEP) and control theoretic frameworks, both of which have been used to analyze a wide variety of first-order methods in optimization.