Class cauchy_point

Instance Methods

__init__(self, func, dfunc=None, d2func=None, args=(), x0=None, func_tol=1e-05, maxiter=1000, full_output=0, print_flag=0, delta_max=100000.0, delta0=1.0, eta=0.2)
Cauchy Point trust-region algorithm.

backup_current_data(self)
Function to backup the current data into fk_last.

calc_pk(self)
Find the Cauchy point.

update_data(self)
Function to update the function value, gradient vector, and hessian matrix

Inherited from generic_trust_region.generic_trust_region: calc_rho, new_param_func

Inherited from generic_minimise.generic_minimise: generic_minimise, tests

Method Details

__init__(self, func, dfunc=None, d2func=None, args=(), x0=None, func_tol=1e-05, maxiter=1000, full_output=0, print_flag=0, delta_max=100000.0, delta0=1.0, eta=0.2)
(Constructor)

Cauchy Point trust-region algorithm.

Page 70 from 'Numerical Optimization' by Jorge Nocedal and Stephen J. Wright, 1999
The Cauchy point is defined by:

                         delta
        pCk  =  - tau_k ------- dfk
                        ||dfk||

where:
        delta_k is the trust region radius,
        dfk is the gradient vector,

                 / 1                                            if dfk . Bk . dfk <= 0
        tau_k = <
                 \ min(||dfk||**2/(delta . dfk . Bk . dfk), 1)  otherwise.

Overrides: generic_minimise.generic_minimise.__init__