Introduction

This is a brief documentation for using Irene. Irene was originally written to find reliable approximations for optimum value of an arbitrary optimization problem. It implements a modification of Lasserre’s SDP Relaxations based on generalized truncated moment problem to handle general optimization problems algebraically.

Documentation Scope

The documentation now covers three complementary pathways for constrained polynomial optimization:

  1. SDP hierarchy methods (moment/SOS based).

  2. Geometric programming relaxations.

  3. SONC relaxations.

The recommended reading path is:

  1. architecture for conceptual map.

  2. algebra and program for representation layer.

  3. sdp, geometric, and sonc for method-specific formulations.

Requirements and dependencies

This is a python package, so clearly python is an obvious requirement. Irene relies on the following packages:

  • for vector calculations:
  • for symbolic computations:
  • for semidefinite optimization, at least one of the following is required:

Dependency Matrix by Method Family

Method family

  • Core Python packages

  • Optional packages

  • External solver requirement
SDP relaxations

  • numpy, scipy, sympy

  • cvxopt

  • one of cvxopt, dsdp, sdpa, csdp
Geometric relaxations

  • numpy, scipy, sympy

  • gpkit

  • gpkit-supported GP backend
SONC relaxations

  • numpy, scipy, sympy

  • gpkit

  • gpkit-supported GP backend

Solver Prerequisites

Before running examples, verify available solvers from Python:

from Irene.base import base
print(base().AvailableSDPSolvers())

Quick Validation Workflow

After installation, the following commands provide a practical smoke test:

python examples/Example01.py
python examples/GPExample.py
python examples/SONCExample.py
python -m unittest discover tests/

Solver Troubleshooting

Common runtime signatures and first actions:

  1. AvailableSDPSolvers() returns an empty list.

    This indicates that no configured SDP backend is currently reachable. Install at least one supported solver and verify it is available on PATH (or configured in solver path settings on platforms that require explicit paths).

  2. RuntimeError: GP solve failed or RuntimeError: SONC GP solve failed.

    These messages usually indicate missing GP backend support, an unavailable solver, or an infeasible/numerically unstable relaxation for the selected formulation. Start with the shipped examples, lower verbosity, and simplified instances.

  3. ModuleNotFoundError: No module named 'gpkit'.

    Install gpkit before running geometric or SONC examples.

  4. SDP solve runs but returns non-optimal status.

    Try another supported SDP solver, inspect constraints for scaling issues, and compare with a lower relaxation order before increasing model complexity.

Download

Irene can be obtained from https://github.com/mghasemi/Irene.

Installation

To install Irene, run the following in terminal:

sudo python setup.py install

Documentation

The documentation of Irene is prepared via sphinx.

To compile html version of the documentation run:

$Irene/doc/make html

To make a pdf file,subject to existence of latexpdf run:

$Irene/doc/make latexpdf

Documentation is also available at http://irene.readthedocs.io.

License

Irene is distributed under MIT license:

MIT License

Copyright (c) 2016-2026 Mehdi Ghasemi

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.