Gauss-Newton Optimization

GaussNewtonOptimizer

Tunable Gauss-Newton optimization routine to find the maximum a posteriori (MAP) estimate under nonlinear observations and a GMRF prior. TODO: Explain parameters.

optimize(optim::GaussNewtonOptimizer)

Iterate until the stopping criterion is fulfilled.

take_step(optim::GaussNewtonOptimizer)

Take a Gauss-Newton step in the optimization process.

GNLinearSolverBlueprint

Abstract type for the specification of a solver for the linear systems arising in Gauss-Newton optimization.

GNCholeskySolverBlueprint(perm)

Specification of a linear solver for Gauss-Newton systems based on the Cholesky decomposition. perm is a node reordering (permutation) to minimize fill-in. If such a reordering is available from previous computations, it can be reused here to avoid unnecessary computational overhead. If perm is not passed, it will be computed during the Cholesky decomposition.

GNCGSolverBlueprint(; maxiter, reltol, abstol, preconditioner_fn, verbose)

Specification of a linear solver for Gauss-Newton systems based on the conjugate gradient (CG) method.

AbstractLineSearch

Abstract type for the specification of a line search scheme for optimization.

BacktrackingLineSearch

Specification of a line search based on backtracking via the Armijo condition. TODO: Description of parameters

NoLineSearch

A type that communicates that no line search will be used, i.e. the initial step proposed by the optimization algorithm is the step that will be taken.

AbstractStoppingCriterion

Abstract type for the specification of a criterion that tells an optimization algorithm when to stop iterating.

NewtonDecrementCriterion(threshold)

Stops the optimization procedure when ∇f(xₖ) ∇²f(xₖ)⁻¹ ∇f(xₖ) < threshold.

StepNumberCriterion(max_steps)

Stops the optimization procedure when a maximum number of iterations / steps is reached.

OrCriterion(criteria)

Stops the optimization procedure when any of the criteria in criteria are fulfilled.