A Manopt problem
A problem describes all static data of an optimisation task and has as a super type
Manopt.AbstractManoptProblem — TypeAbstractManoptProblem{M<:AbstractManifold}Describe a Riemannian optimization problem with all static (not-changing) properties.
The most prominent features that should always be stated here are
- the
AbstractManifold$\mathcal M$ - the cost function $f: \mathcal M → ℝ$
Usually the cost should be within an AbstractManifoldObjective.
Manopt.get_objective — Functionget_objective(o::AbstractManifoldObjective, recursive=true)return the (one step) undecorated AbstractManifoldObjective of the (possibly) decorated o. As long as your decorated objective stores the objective within o.objective and the dispatch_objective_decorator is set to Val{true}, the internal state are extracted automatically.
By default the objective that is stored within a decorated objective is assumed to be at o.objective. Overwrite _get_objective(o, ::Val{true}, recursive) to change this behaviour for your objectiveo` for both the recursive and the direct case.
If recursive is set to false, only the most outer decorator is taken away instead of all.
get_objective(mp::AbstractManoptProblem, recursive=false)return the objective AbstractManifoldObjective stored within an AbstractManoptProblem. If recursive is set to true, it additionally unwraps all decorators of the objective
get_objective(amso::AbstractManifoldSubObjective)Return the (original) objective stored the sub objective is build on.
Manopt.get_manifold — Functionget_manifold(amp::AbstractManoptProblem)return the manifold stored within an AbstractManoptProblem
Usually, such a problem is determined by the manifold or domain of the optimisation and the objective with all its properties used within an algorithm, see The Objective. For that one can just use
Manopt.DefaultManoptProblem — TypeDefaultManoptProblem{TM <: AbstractManifold, Objective <: AbstractManifoldObjective}Model a default manifold problem, that (just) consists of the domain of optimisation, that is an AbstractManifold and an AbstractManifoldObjective
For the constraint optimisation, there are different possibilities to represent the gradients of the constraints. This can be done with a
ConstraintProblemThe primal dual-based solvers (Chambolle-Pock and the PD Semi-smooth Newton), both need two manifolds as their domains, hence there also exists a
Manopt.TwoManifoldProblem — TypeTwoManifoldProblem{
MT<:AbstractManifold,NT<:AbstractManifold,O<:AbstractManifoldObjective
} <: AbstractManoptProblem{MT}An abstract type for primal-dual-based problems.
From the two ingredients here, you can find more information about