pymor.algorithms.line_search

Module Contents

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)

Unconstrained Armijo line search algorithm.

This method computes a step size such that the unconstrained 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 as either a VectorArray or a NumPy array.

• initial_value – Value of f in the point starting_point.

• 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.

• iterations – Number of total Armijo line search iterations.

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

Constrained Armijo line search algorithm.

This method computes a step size such that the given constrained Armijo condition 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.

• armijo_condition – A callable used as the Armijo termination condition during the step length computation.

• grad – Gradient of f in the point starting_point as either a VectorArray or a NumPy array.

• initial_value – Value of f in the point starting_point.

• 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.

• iterations – Number of total Armijo line search iterations.