backtrack(func,
args,
x,
f,
g,
p,
a_init=1.0,
rho=0.5,
c=0.0001,
max_iter=500)
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Backtracking line search.
Procedure 3.1, page 41, from 'Numerical Optimization' by Jorge Nocedal
and Stephen J. Wright, 1999, 2nd ed.
Requires the gradient vector at point xk.
Internal variables
ai - The step length at line search iteration i. xai - The
parameter vector at step length ai. fai - The function value at step
length ai.
- Parameters:
func (func) - The function to minimise.args (tuple) - The tuple of arguments to supply to the functions func.x (numpy rank-1 array) - The parameter vector.f (float) - The function value at the point x.g (numpy rank-1 array) - The gradient vector at the point x.p (numpy rank-1 array) - The descent direction.a_init (float) - Initial step length.rho (float) - The step length scaling factor (should be between 0 and 1).c (float) - Constant between 0 and 1 determining the slope for the sufficient
decrease condition.maxiter (int) - The maximum number of iterations. - Returns: numpy rank-1 array
- The parameter vector, minimised along the direction xk + ak.pk,
to be used at k+1.
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