Module nocedal_wright_wolfe

A line search algorithm implemented using the strong Wolfe conditions.

This file is part of the minfx optimisation library.

Functions

nocedal_wright_wolfe(func, func_prime, args, x, f, g, p, a_init=1.0, max_a=100000.0, mu=0.001, eta=0.9, tol=1e-10, print_flag=0)
A line search algorithm implemented using the strong Wolfe conditions.

print_data(text, k, a)
Temp func for debugging.

zoom(func, func_prime, args, f_count, g_count, x, f, g, p, mu, eta, i, a0, a_lo, a_hi, tol, print_flag=0)
Find the minimum function value in the open interval (a_lo, a_hi)

Variables

__package__ = 'minfx.line_search'

Imports: deepcopy, dot, sqrt, cubic_ext, quadratic_fafbga, quadratic

Function Details

nocedal_wright_wolfe(func, func_prime, args, x, f, g, p, a_init=1.0, max_a=100000.0, mu=0.001, eta=0.9, tol=1e-10, print_flag=0)

A line search algorithm implemented using the strong Wolfe conditions.

Algorithm 3.2, page 59, from 'Numerical Optimization' by Jorge Nocedal and Stephen J. Wright, 1999, 2nd ed.

Requires the gradient function.

These functions require serious debugging and recoding to work properly (especially the safeguarding)!

Parameters:

• func (func) - The function to minimise.
• func_prime (func) - The function which returns the gradient vector.
• args (args) - The tuple of arguments to supply to the functions func and dfunc.
• x (numpy array) - The parameter vector at minimisation step k.
• f (float) - The function value at the point x.
• g (numpy array) - The function gradient vector at the point x.
• p (numpy array) - The descent direction.
• a_init (flaot) - Initial step length.
• a_max (float) - The maximum value for the step length.
• mu (float) - Constant determining the slope for the sufficient decrease condition (0 < mu < eta < 1).
• eta (float) - Constant used for the Wolfe curvature condition (0 < mu < eta < 1).
• tol (float) - The function tolerance.
• print_flag (int) - The higher the value, the greater the amount of info printed out.

zoom(func, func_prime, args, f_count, g_count, x, f, g, p, mu, eta, i, a0, a_lo, a_hi, tol, print_flag=0)

Find the minimum function value in the open interval (a_lo, a_hi)

Algorithm 3.3, page 60, from 'Numerical Optimization' by Jorge Nocedal and Stephen J. Wright, 1999, 2nd ed.