Unconstrained Predictor-Corrector

class kona.algorithms.PredictorCorrector(primal_factory, state_factory, eq_factory=None, ineq_factory=None, optns=None)[source]

Bases: kona.algorithms.base_algorithm.OptimizationAlgorithm

A reduced-space Newton-Krylov algorithm for PDE-governed unconstrained optimization, globalized in a predictor-corrector homotopy path following framework.

This implementation is loosely based on the predictor-corrector method described by `Brown and Zingg<http://www.sciencedirect.com/science/article/pii/S0021999116301760>`_ for nonlinear computational fluid dynamics problems.

The homotopy map used in this algorithm is given as:

\[\begin{split}\\mathcal{H}(x, u) = (1-\lambda) F(x, u) + \lambda\end{split}\]

rac{1}{2}(x - x_0)^T(x - x_0)

where \(x_0\) is the initial design point.

factor_matrices : bool
Boolean flag for matrix-based PDE solvers.
lamb, inner_tol, step, nom_dcurv, nom_angl, max_factor, min_factor : float
Homotopy parameters.
scale, grad_scale, feas_scale : float
Optimality metric normalization factors.
hessian : ReducedHessian
Matrix object defining the Hessian matrix-vector product.
precond : BaseHessian-like
Matrix object defining the approximation to the Hessian inverse.
krylov : FGMRES
A krylov solver object used to solve the system defined by the Hessian.