Requirements

Core runtime (from pyproject.toml):

• Python >= 3.10

• sympy, numpy, scipy

• cvxpy, cvxopt

• gpkit, multiprocess

Optional extras:

• .[symengine] for SymEngine acceleration

• .[solvers] for additional conic/QP solvers (clarabel, scs, osqp)

• .[dev] for testing and coverage tooling

Symbolic backend selection:

• IRENE_SYMBOLIC_BACKEND=symengine (default when available)

• IRENE_SYMBOLIC_BACKEND=sympy

• IRENE_SYMBOLIC_BACKEND=auto

Installation

From PyPI:

pip install irene

or from source (development):

pip install .[symengine,solvers]

Development dependencies:

pip install .[dev,symengine,solvers]

Testing

Run test suites configured in pyproject.toml:

pytest

The project includes tests under Irene/tests/ and tests/.

Quick Start (Modern API)

from Irene.grouprings import CommutativeSemigroup, SemigroupAlgebra
from Irene.program import OptimizationProblem
from Irene.relaxation_api import RelaxationEngine

sg = CommutativeSemigroup(["x", "y", "z"])
sga = SemigroupAlgebra(sg)
x, y, z = sga["x"], sga["y"], sga["z"]

prog = OptimizationProblem(sga)
prog.set_objective(-2*x + y - z)
prog.add_constraint(x + y + z <= 4)
prog.add_constraint(x >= 0)

engine = RelaxationEngine(prog, order=2, solver="cvxpy")
result = engine.solve("sos")
print(result.status, result.value)

Legacy API Compatibility

The legacy API remains available for backward compatibility (for example SDPRelaxations). For new code, prefer OptimizationProblem + RelaxationEngine.

Documentation

Read the hosted documentation at irene.readthedocs.io. Documentation sources are in doc/ and include architecture, migration, solver, and benchmark chapters.

Build docs locally:

make -C doc html

Related Work

The theoretical foundations of the relaxation hierarchies implemented here are developed in:

• 13. Ghasemi, J. B. Lasserre, M. Marshall, Lower Bounds on the Global Minimum of a Polynomial, Computational Optimization and Applications 56(1), 2013. arXiv:1209.3049

• 13. Ghasemi, M. Marshall, Lower Bounds for Polynomials Using Geometric Programming, SIAM Journal on Optimization 22(2), 460–473, 2012. DOI:10.1137/110836869

License

Irene is distributed under the MIT License.