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 […].