PEPFlow: A library for the systematic analysis of optimization algorithms

Abstract

Optimization underpins modern science, engineering, and technology. Solving an optimization problem involves two key stages: formulating a real-world task as a mathematical model and designing algorithms to solve it efficiently. While disciplined convexity modeling has been automated by tools such as the CVX family, the analysis of convex-optimization algorithms remains challenging and often requires deep expertise.

This talk introduces PEPFlow, a Python library based on the Performance Estimation Problem (PEP) framework, which formulates convergence behavior of an algorithm as a tractable convex optimization problem. Several open-source packages, such as PEPit and PESTO, have already demonstrated the power of the PEP approach in studying optimization algorithms.

PEPFlow offers new features including interactivity and symbolic calculation. It provides an intuitive environment for constructing and exploring both primal and dual PEPs, interacting with sparsity patterns of dual variables, and even attempting to derive symbolic proofs of convergence. Together, these features aim to make the study and teaching of optimization algorithms more disciplined, systematic, and exploratory.

Bio

Xin Jiang is an Assistant Professor of Industrial and Systems Engineering at the University of Houston. He earned his Ph.D. in Electrical and Computer Engineering from UCLA, advised by Prof. Lieven Vandenberghe, and completed postdoctoral research with Prof. Frank E. Curtis at Lehigh University and Prof. Adrian S. Lewis at Cornell University. Xin’s research centers on the theory and algorithms of large-scale optimization arising in engineering and data science. He is particularly interested in exploiting problem structure in nonsmooth optimization and designing tailored algorithms for large-scale systems.