Module cauchy_point

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.

Imports: dot, sqrt, Trust_region, Min

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,

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