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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.
Options ------- inexact : bool, optional Accuracy to solve subproblems. If True requires less nonlinear iterations, but more vector products.
.. versionadded:: 1.0.0 """
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) |