AutoLyap

A Python package for automated Lyapunov-based convergence analyses of first-order optimization and inclusion methods.

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Overview

AutoLyap streamlines the process of constructing and verifying Lyapunov analyses by formulating them as semidefinite programs (SDPs). It supports a broad class of structured optimization and inclusion problems, providing computer-assisted proofs of linear or sublinear convergence rates for many well‑known algorithms.

A typical workflow:

1. Choose the class of optimization/inclusion problems.
2. Choose the first-order method to analyze.
3. Choose the type of Lyapunov analysis to search for or verify (which implies a convergence or performance conclusion).

AutoLyap builds the underlying SDP and solves it through configurable backend solvers.

Documentation

• User docs: https://autolyap.github.io
• Contributing guide: https://autolyap.github.io/contributing/
• Developer commands (internal): DEVELOPER_COMMANDS.md
• Changelog: CHANGELOG.md
• Release process (maintainers): RELEASING.md
• License: LICENSE

Cite this project

If AutoLyap contributes to your research or software, please cite:

• Upadhyaya, Manu; Das Gupta, Shuvomoy; Taylor, Adrien B.; Banert, Sebastian; Giselsson, Pontus (2026). The AutoLyap software suite for computer-assisted Lyapunov analyses of first-order methods. arXiv:2506.24076.

@misc{upadhyaya2026autolyap,
  author = {Upadhyaya, Manu and Das Gupta, Shuvomoy and Taylor, Adrien B. and Banert, Sebastian and Giselsson, Pontus},
  title = {The {AutoLyap} software suite for computer-assisted {L}yapunov analyses of first-order methods},
  year = {2026},
  archivePrefix = {arXiv},
  eprint = {2506.24076},
  primaryClass = {math.OC},
}