Equality Constrained Predictor-Corrector

class kona.algorithms.PredictorCorrectorCnstr(primal_factory, state_factory, eq_factory=None, ineq_factory=None, optns=None)

Bases: kona.algorithms.base_algorithm.OptimizationAlgorithm

A reduced-space Newton-Krylov algorithm for PDE-governed equality constrained 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:

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

rac{1}{2} left[

(x - x_0)^T(x - x_0) - (lambda - lambda_0)^T(lambda - lambda_0)

where \(x_0\) is the initial design point and \(\lambda_0\) is the initial Lagrange multipliers.

factor_matrices : bool

Boolean flag for matrix-based PDE solvers.

mu, 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 : ReducedKKTMatrix

Matrix object defining the KKT matrix-vector product.

precond : BaseHessian-like

Matrix object defining the approximation to the Hessian inverse.

krylov : FGMRES

Krylov solver object used to solve the system defined by the KKT matrix-vector product.

solve()