pymor.algorithms.bfgs

Module Contents

pymor.algorithms.bfgs.error_aware_bfgs(model, parameter_space=None, initial_guess=None, miniter=0, maxiter=100, rtol_output=1e-16, rtol_mu=1e-16, tol_sub=1e-08, line_search_params=None, stagnation_window=3, stagnation_threshold=np.inf, error_aware=False, error_criterion=None, line_search_error_criterion=None)[source]

BFGS algorithm.

This method solves the optimization problem

min J(mu), mu in C

for a model with an output functional \(J\) depending on a box-constrained mu using the BFGS method.

In contrast to scipy.optimize.minimize with the L-BFGS-B methods, this BFGS implementation is explicitly designed to work with an error estimator. In particular, this implementation terminates if the higher level TR boundary from pymor.algorithms.tr is reached instead of continuing to optimize close to the boundary.

Parameters:

  • model – The Model with output J used for the optimization.

  • parameter_space – If not None, the ParameterSpace for enforcing the box constraints on the parameter values mu. Otherwise a ParameterSpace with lower bound -1 and upper bound 1.

  • initial_guess – If not None, parameter values containing an initial guess for the solution mu. Otherwise, random parameter values from the parameter space are chosen as the initial value.

  • miniter – Minimum amount of iterations to perform.

  • maxiter – Fail if the iteration count reaches this value without converging.

  • rtol_output – Finish when the relative error measure of the output is below this threshold.

  • rtol_mu – Finish when the relative error measure of the parameter values is below this threshold.

  • tol_sub – Finish when the first order criticality is below this threshold.

  • line_search_params – Dictionary of additional parameters passed to the Armijo line search method.

  • stagnation_window – Finish when the parameter update has not been enlarged by a factor of stagnation_threshold during the last stagnation_window iterations.

  • stagnation_threshold – See stagnation_window.

  • error_aware – If True, perform an additional error aware check during the line search phase. Intended for use with the trust region algorithm.

  • error_criterion – The additional error criterion used to check model confidence. This maps parameter values and an output value to a boolean indicating if the criterion is fulfilled. Refer to function error_aware_bfgs_criterion in pymor.algorithms.tr.trust_region for an example.

  • line_search_error_criterion – The additional error criterion used to check model confidence in the line search. This maps parameter values and an output value to a boolean indicating if the criterion is fulfilled. Refer to function error_aware_line_search_criterion in pymor.algorithms.tr.trust_region for an example.

Returns:

  • mu – NumPy array containing the computed parameter values.

  • data – Dict containing the following fields:

    mus:

    list of parameter values after each iteration.

    foc_norms:

    NumPy array of the first order criticality norms after each iteration.

    update_norms:

    NumPy array of the norms of the update vectors after each iteration.

    iterations:

    Number of total BFGS iterations.

    line_search_iterations:

    NumPy array of the number of line search iterations per BFGS iteration.

Raises:

BFGSError – Raised if the BFGS algorithm failed to converge.