Module cauchy_point

Cauchy Point trust region nonlinear optimization.

This file is part of the minfx optimisation library.

Classes

Cauchy_point

Functions

cauchy_point(func=None, dfunc=None, d2func=None, args=(), x0=None, func_tol=1e-25, grad_tol=None, maxiter=1000000.0, delta_max=100000.0, delta0=1.0, eta=0.2, full_output=0, print_flag=0, print_prefix='')
Cauchy Point trust region algorithm.

Variables

__package__ = 'minfx'

Imports: dot, sqrt, Min, Trust_region

Function Details

cauchy_point(func=None, dfunc=None, d2func=None, args=(), x0=None, func_tol=1e-25, grad_tol=None, maxiter=1000000.0, delta_max=100000.0, delta0=1.0, eta=0.2, full_output=0, print_flag=0, print_prefix='')

Cauchy Point trust region algorithm.

Page 69 from 'Numerical Optimization' by Jorge Nocedal and Stephen J. Wright, 1999, 2nd ed. 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,

and:

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