scipy.optimize.line_search¶

scipy.optimize.line_search(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)[source]¶

Find alpha that satisfies strong Wolfe conditions.

Parameters:

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+alphapk)`, 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.

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.

Notes

Uses the line search algorithm to enforce strong Wolfe conditions. See Wright and Nocedal, ‘Numerical Optimization’, 1999, pg. 59-60.

For the zoom phase it uses an algorithm by […].