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