The Manopt.jl problem

AbstractManoptProblem{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.

get_cost(amp::AbstractManoptProblem, p)

Evaluate the cost function f stored within the AbstractManifoldObjective of an AbstractManoptProblem amp at the point p.

get_gradient(amp::AbstractManoptProblem, p)
get_gradient!(amp::AbstractManoptProblem, X, p)

Evaluate the gradient of an AbstractManoptProblem amp at the point p.

This can also be computed in-place of X for the !-variant.

Y = get_hessian(amp::AbstractManoptProblem, p, X)
get_hessian!(amp::AbstractManoptProblem, Y, p, X)

Evaluate the Hessian of an AbstractManoptProblem amp at p applied to a tangent vector X, computing $\operatorname{Hess}f(p)[X]$, which can also happen in-place of Y.

get_manifold(amp::AbstractManoptProblem)

Return the manifold stored within an AbstractManoptProblem.

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_preconditioner(amp::AbstractManoptProblem, p, X)

Evaluate the preconditioner of the objective of the AbstractManoptProblem amp at the point p, applied to the tangent vector X.

It usually is a symmetric, positive definite approximation of the inverse of the Hessian of the cost function f.

X = get_subtrahend_gradient(amp, p)
get_subtrahend_gradient!(amp, X, p)

Evaluate the (sub)gradient of the subtrahend h from within the ManifoldDifferenceOfConvexObjective of an AbstractManoptProblem amp at the point p.

The evaluation is done in place of X for the !-variant. An objective using AllocatingEvaluation might still allocate memory within. When the non-mutating variant is called with an InplaceEvaluation, memory for the result is allocated.

set_parameter!(amp::AbstractManoptProblem, element::Symbol, field::Symbol, value)

Set a certain field/element from the AbstractManoptProblem amp to value. This function usually dispatches on Val(element). Instead of a single field, also a chain of elements can be provided, allowing access to encapsulated parts of the problem.

Main values for element are :Manifold and :Objective.