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$\mathcal M$ (cf. ManifoldsBase.jl#AbstractManifold) - the cost function $f\colon \mathcal M → ℝ$
Usually the cost should be within an AbstractManifoldObjective.
Manopt.get_objective — Functionget_objective(mp::AbstractManoptProblem)return the objective AbstractManifoldObjective stored within an AbstractManoptProblem.
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 we 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
The exception to these are the primal dual-based solvers (Chambolle-Pock and the PD Semismooth Newton]), which both need two manifolds as their domain(s), hence thre 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
- the
AbstractManifoldin ManifoldsBase.jl - the
AbstractManifoldObjectiveon the page about the objective.