pymor.algorithms.line_search

Module Contents

Functions

armijo

Armijo line search algorithm.

pymor.algorithms.line_search.armijo(f, starting_point, direction, grad=None, initial_value=None, alpha_init=1.0, tau=0.5, beta=0.0001, maxiter=10)

Armijo line search algorithm.

This method computes a step size such that the Armijo condition (see [NW06], p. 33) is fulfilled.

Parameters

f

Real-valued function that can be evaluated for its value.

starting_point

A VectorArray of length 1 containing the starting point of the line search.

direction

Descent direction along which the line search is performed.

grad

Gradient of f in the point starting_point.

initial_value

Value of f in the point starting_point.

alpha_init

Initial step size that is gradually reduced.

tau

The fraction by which the step size is reduced in each iteration.

beta

Control parameter to adjust the required decrease of the function value of f.

maxiter

Use alpha_init as default if the iteration count reaches this value without finding a point fulfilling the Armijo condition.

Returns

alpha

Step size computed according to the Armijo condition.