PolynomialOptimization is a Julia package that allows to easily optimize large-scale polynomial optimization problems
(currently commutative only).
It builds on MultivariatePolynomials to provide a concise interface for the specification of the problem and allows to apply
many kinds of sparsity methods. It also fully supports complex-valued problems and positive semidefinite constraints and allows
to extract solutions even for sparse problems.
It directly interfaces the solvers
Clarabel,
COPT,
Hypatia,
Mosek,
ProxSDP, and
SCS without using JuMP, avoiding this bottleneck so that indeed almost all the time is spent
in the solver, not in the problem formulation. It also features new research-level solvers: an own implementation of the
primal spectral bundling method and the SketchyCGAL
algorithm; an efficiency-oriented refactoring of the low-rank solver Loraine,
and an interface to the experimental LoRADS solver.