Irene

Irene is a Python toolkit for constrained polynomial optimization over commutative real algebras.

It supports multiple relaxation families and backends:

• SOS and moment-SDP relaxations
• SONC relaxations
• hybrid SOS+SONC workflows
• legacy and CVXPY-based SDP solver paths

Repository Status (2026-08-09)

• Development status: active
• Packaging target: 2.0.0.dev0 (defined in pyproject.toml)
• Phases 1-3 modernization work: completed
• Current focus: integration hardening, CI/benchmark automation, and remaining reduction wiring

Implemented modernization highlights in this repository:

• Selectable symbolic backend via IRENE_SYMBOLIC_BACKEND (SymEngine primary, SymPy fallback)
• CVXPY solver abstraction layer (with Clarabel/SCS/CVXOPT integration)
• Structural reduction modules:
  • border basis
  • correlative sparsity detection
  • Newton polytope pruning
• Unified relaxation entrypoint in Irene/relaxation_api.py
• Runtime telemetry helpers in Irene/telemetry.py

Known current gap:

• Phase 3 reduction modules are implemented and tested, but full end-to-end integration through all legacy relaxations.py code paths is still in progress.

Reduction defaults:

• Structural reductions are opt-in for compatibility. Pass RelaxationConfig to RelaxationEngine to enable Newton-polytope pruning, border-basis reduction, or correlative sparsity detection.

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

Create and activate a virtual environment, then install from source.

Base install:

pip install .

Install with SymEngine + solver extras:

pip install .[symengine,solvers]

Install 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

License

Irene is distributed under the MIT License.