line_search_wolfe2(f, myfprime, xk, pk, gfk=None, old_fval=None, old_old_fval=None, args=(), c1=0.0001, c2=0.9, amax=None, extra_condition=None, maxiter=10)

Notes

Uses the line search algorithm to enforce strong Wolfe conditions. See Wright and Nocedal, 'Numerical Optimization', 1999, pp. 59-61.

Parameters

f : callable f(x,*args)

Objective function.

myfprime : callable f'(x,*args)

Objective function gradient.

xk : ndarray

Starting point.

pk : ndarray

Search direction.

gfk : ndarray, optional

Gradient value for x=xk (xk being the current parameter estimate). Will be recomputed if omitted.

old_fval : float, optional

Function value for x=xk. Will be recomputed if omitted.

old_old_fval : float, optional

Function value for the point preceding x=xk.

args : tuple, optional

Additional arguments passed to objective function.

c1 : float, optional

Parameter for Armijo condition rule.

c2 : float, optional

Parameter for curvature condition rule.

amax : float, optional

Maximum step size

extra_condition : callable, optional

A callable of the form extra_condition(alpha, x, f, g) returning a boolean. Arguments are the proposed step alpha and the corresponding x , f and g values. The line search accepts the value of alpha only if this callable returns True . If the callable returns False for the step length, the algorithm will continue with new iterates. The callable is only called for iterates satisfying the strong Wolfe conditions.

maxiter : int, optional

Maximum number of iterations to perform.

Returns

alpha : float or None

Alpha for which x_new = x0 + alpha * pk , or None if the line search algorithm did not converge.

fc : int

Number of function evaluations made.

gc : int

Number of gradient evaluations made.

new_fval : float or None

New function value f(x_new)=f(x0+alpha*pk) , or None if the line search algorithm did not converge.

old_fval : float

Old function value f(x0) .

new_slope : float or None

The local slope along the search direction at the new value <myfprime(x_new), pk> , or None if the line search algorithm did not converge.

Find alpha that satisfies strong Wolfe conditions.

Examples

>>> from scipy.optimize import line_search

A objective function and its gradient are defined.

>>> def obj_func(x):
...     return (x[0])**2+(x[1])**2
... def obj_grad(x):
...     return [2*x[0], 2*x[1]]

We can find alpha that satisfies strong Wolfe conditions.

>>> start_point = np.array([1.8, 1.7])
... search_gradient = np.array([-1.0, -1.0])
... line_search(obj_func, obj_grad, start_point, search_gradient)
(1.0, 2, 1, 1.1300000000000001, 6.13, [1.6, 1.4])

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.optimize._linesearch.line_search_wolfe2

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