_trustregion_krylov.py
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from ._trustregion import (_minimize_trust_region)
from ._trlib import (get_trlib_quadratic_subproblem)
__all__ = ['_minimize_trust_krylov']
def _minimize_trust_krylov(fun, x0, args=(), jac=None, hess=None, hessp=None,
inexact=True, **trust_region_options):
"""
Minimization of a scalar function of one or more variables using
a nearly exact trust-region algorithm that only requires matrix
vector products with the hessian matrix.
.. versionadded:: 1.0.0
Options
-------
inexact : bool, optional
Accuracy to solve subproblems. If True requires less nonlinear
iterations, but more vector products.
"""
if jac is None:
raise ValueError('Jacobian is required for trust region ',
'exact minimization.')
if hess is None and hessp is None:
raise ValueError('Either the Hessian or the Hessian-vector product '
'is required for Krylov trust-region minimization')
# tol_rel specifies the termination tolerance relative to the initial
# gradient norm in the Krylov subspace iteration.
# - tol_rel_i specifies the tolerance for interior convergence.
# - tol_rel_b specifies the tolerance for boundary convergence.
# in nonlinear programming applications it is not necessary to solve
# the boundary case as exact as the interior case.
# - setting tol_rel_i=-2 leads to a forcing sequence in the Krylov
# subspace iteration leading to quadratic convergence if eventually
# the trust region stays inactive.
# - setting tol_rel_b=-3 leads to a forcing sequence in the Krylov
# subspace iteration leading to superlinear convergence as long
# as the iterates hit the trust region boundary.
# For details consult the documentation of trlib_krylov_min
# in _trlib/trlib_krylov.h
#
# Optimality of this choice of parameters among a range of possibilities
# has been tested on the unconstrained subset of the CUTEst library.
if inexact:
return _minimize_trust_region(fun, x0, args=args, jac=jac,
hess=hess, hessp=hessp,
subproblem=get_trlib_quadratic_subproblem(
tol_rel_i=-2.0, tol_rel_b=-3.0,
disp=trust_region_options.get('disp', False)
),
**trust_region_options)
else:
return _minimize_trust_region(fun, x0, args=args, jac=jac,
hess=hess, hessp=hessp,
subproblem=get_trlib_quadratic_subproblem(
tol_rel_i=1e-8, tol_rel_b=1e-6,
disp=trust_region_options.get('disp', False)
),
**trust_region_options)