`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)[source]¶

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)[source]¶

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.

pymor.algorithms.line_search¶

Module Contents¶

`pymor.algorithms.line_search`¶