PEPFlow: A Python Library for the Workflow of Performance Estimation of Optimization Algorithms

We present PEPFlow, a Python library designed to streamline the workflow for analyzing the convergence behavior of a variety of first-order optimization algorithms. The library builds on Performance Estimation Problems (PEPs), which reformulate the worst-case convergence guarantees as convex semidefinite programs (SDPs). Solving the SDP provides numerical evidence of convergence rates, and more importantly, its dual variables can be leveraged to construct analytical proofs. PFPFlow supports the entire workflow by automating SDP formulation, exploring relaxations, inspecting dual variables, and verifying proofs. Together, these features bridge numerical verification with rigorous analysis and substantially reduce manual effort. A pre-release version of PEPFlow is available at: https://github.com/pepflow-lib/PEPFlow.