A Linear Parameter-Varying Framework for the Analysis of Time-Varying Optimization Algorithms

This repository contains the code from our paper

Jakob, Fabian, and Andrea Iannelli. "A Linear Parameter-Varying Framework for the Analysis of Time-Varying Optimization Algorithms." arXiv preprint. arXiv:2501.07461 (2025).

Installation

The repo has been developed and tested with Python 3.11 and the dependencies given in requirements.txt

pip install -r requirements.txt

You may also use open source SDP solvers such as CVXOPT. However, the numeric results are most robust using Mosek, which can be used with an academic license:

pip install Mosek

Notebooks

Demonstrates the use of the repo; reproduces the plots in the paper.

tracking_certificates.ipynb: Algorithm certificates across problem parameters

tracking_bounds.ipynb: Certified tracking error bounds for a given objective and algorithm

Repository Structure

src/
├── tracking_certificates.ipynb
├── tracking_bounds.ipynb
├── lib/
│   ├── algorithms/
│   │   ├── unconstrained.py
│   │   └── constrained.py
│   ├── analysis/
│   │   ├── lure.py
│   │   ├── lyapunov.py
│   │   ├── polytope.py
│   │   ├── solver.py
│   │   └── run_solver.py
│   ├── simulation/
│   │   ├── algorithm.py
│   │   ├── objectives.py
│   │   └── simulate.py
│   └── utils/
│       └── plot.py
└── tests/

Running Tests

pytest src/tests/

Tests cover algorithms, objectives, IQC builders, Lyapunov matrices, polytope utilities, and simulation outputs (89 tests). Tests that invoke the MOSEK/CVXPY solver are marked slow and skipped by default; run them with pytest -m slow.

Contact

Fabian Jakob — fabian.jakob@ist.uni-stuttgart.de