Welcome to Irene’s Documentation!¶
Irene is a Python toolkit for polynomial optimization via semidefinite programming, geometric programming, and SONC/SOS hierarchies. It implements Lasserre’s moment-SDP hierarchy, circuit-based SONC relaxations, mean polynomial forms, correlative sparsity detection, Newton polytope pruning, and differential SDP extensions.
Contents:
Getting Started
Core Modules
Phase 3 — Algebraic Reductions
Transcendental & Differential Algebraic Optimization
Solver Layer & Numerical Methods
Benchmarks and Examples
Reference
- Code Documentation
LaTeX()baseCalpha_()Calpha__()MomRelaxationConfigSDPRelaxationsSDRelaxSolsdpOptimizationProblemAtomicSGElementCommutativeSemigroupSemigroupAlgebraSemigroupAlgebraElementGPRelaxationsSONCRelaxations- SOS+SONC Relaxation Framework
SOSONCRelaxSolSOSONCRelaxationssosonc_bounds()BorderBasisCorrelativeSparsityUnionFinddetect_sparsity_from_polys()detect_sparsity_from_problem()NewtonPrunercombined_newton_polytope()minkowski_sum()newton_polytope()prune_basis_from_polys()prune_basis_from_problem()scale_polytope()- Unified Relaxation API
RelaxMethodRelaxResultRelaxationEnginecompare_all()relax()- NOTATION (paper sections referenced)
Algorithm1ResultRankTestResultSparseBorderBasisSparseMomentResultSparseMomentSDPSparseRootsResultToricSetupdeg_A()moment_indices()prolongations()recover_all_sparse_roots()semigroup_level_map()solve_algorithm1()solve_sparse_real_roots()test_theorem_327()toric_ideal()SymbolicEnginefallback_to_sympy()get_symbolic_backend()set_symbolic_backend()to_symengine()to_sympy()CvxpySDPSolverSDPResultavailable_solvers()DSDPKKTRelaxationDSDPMeanRelaxationDSDPRelaxations- Public API
- Usage example
PhaseTimingTelemetryContextTelemetryRecordclear_telemetry()export_json()get_active_record()get_telemetry()timed()find_psd_gram_matrix()get_gram_matrix()is_psd_numeric()is_psd_symbolic()numpy_to_latex()InvariantPolynomial
- Doctest Integration
- Revision History
- Appendix