Module ncg

Classes

Ncg

Functions

ncg(func=None, dfunc=None, d2func=None, args=(), x0=None, min_options=None, func_tol=1e-25, grad_tol=None, maxiter=1000000.0, a0=1.0, mu=0.0001, eta=0.9, full_output=0, print_flag=0, print_prefix='')
Line search Newton conjugate gradient algorithm.

Imports: inverse, Float64, dot, matrixmultiply, sqrt, zeros, Line_search, Min

Function Details

ncg(func=None, dfunc=None, d2func=None, args=(), x0=None, min_options=None, func_tol=1e-25, grad_tol=None, maxiter=1000000.0, a0=1.0, mu=0.0001, eta=0.9, full_output=0, print_flag=0, print_prefix='')

Line search Newton conjugate gradient algorithm.

Page 140 from 'Numerical Optimization' by Jorge Nocedal and Stephen J. Wright, 1999, 2nd ed.

The algorithm is:

Given initial point x0.
while 1:
    Compute a search direction pk by applying the CG method to Hk.pk = -gk, starting from
        x0 = 0.  Terminate when ||rk|| <= min(0.5,sqrt(||gk||)), or if negative curvature is
        encountered.
    Set xk+1 = xk + ak.pk, where ak satisfies the Wolfe, Goldstein, or Armijo backtracking
        conditions.