Parameters for limited step length BFGS algorithm. More...

Public Attributes
Scalar	machine_epsilon
	machine epsilon adjust if needed

unsigned	max_iterations = 10000
	maximum number of iterations of the BFGS algorithm

Scalar	gradient_tolerance

Scalar	alpha_min
	minimum allowed step length

Scalar	wolfe_c1 {1e-4}
	c1 for first Wolfe condition (sufficient decrease)

Scalar	wolfe_c2 {0.9}
	c2 for second Wolfe condition (curvature condition)

Scalar	sigma2 {0.6}
	parameter sigma2 for damped BFGS update

Scalar	sigma3 {3.0}
	parameter sigma3 for damped BFGS update

Scalar	sigma4 {0.0}
	parameter sigma4 for damped BFGS update

Scalar	check_epsilon
	parameter for checking the numerical stability

Scalar	min_change

unsigned	min_iterations_with_no_change = 2
	the number of iterations the criterion above must hold

Scalar	min_grad_param

Scalar	min_value
	termination criterion for minimal function value (stopping value);

Linesearch	linesearch = Linesearch::Backtracking
	line search method (currently no choice)

unsigned	max_linesearch_iterations = std::numeric_limits<unsigned>::max()
	maximum number of linesearch iterations

unsigned	m = 10
	maximum history to store in limited memory methods

bool	allow_restarts = true
	allow the restarting in case of errors

Alpha0Policy	alpha0 = Alpha0Policy::Constant
	how to select alpha0 for start of line search

Friends
template<typename U >
OptimizationParameters< U >	getOptimizationParameters ()
	Get optimization parameters for this type. More...

Detailed Description

Parameters for limited step length BFGS algorithm.

Warning: You can't instantiate this class directly, but you have to use getOptimizationParameters.

Note

If the initialization of the scalar constants is not appropriate for your scalar you can specialize the complete parameter template.

We provide five different termination criteria. The first fulfilled criterion triggers the termination.

Maximum number of iterations (default: 10000). The algorithm terminates after the given number of iterations of the Quasi-Newton method.
Gradient norm (default for double: 1e-6). The algorithm terminates the gradient norm fulfills ||grad|| <= tolerance * max(1.0, ||x||) This is the classical termination criterion.
Minimum change (default for double: 0.0). The algorithm terminates if the relative change in the function value is smaller than this value. Please note that this criterion is also active even if it is set to 0.0: In this case the algorithm terminates if the relative change in the objective function value is so small that it can't be detected anymore. To deactivate this criterion completely, set the value min_iterations_with_no_change to a large value (e.g. UINT_MAX).
Minimum function value (default: -infinity). The algorithm terminates if the objective function value falls below the minimum function value. This criterion is turned off by default. It is mainly useful for comparing optimization algorithms.
Minimum change of gradient or parameters (default for double: machine epsilon). The algorithm terminates if the L2-norm of the gradient change or the parameter change is less than this parameter. If set to a small value (e.g. machine epsilon) it is rarely triggered, however, prevents numerical problems arising from very small changes of the gradient or the parameter set.

Friends And Related Function Documentation

template<typename Scalar>

template<typename U >

OptimizationParameters<U> getOptimizationParameters ( )

friend

Get optimization parameters for this type.

Template Parameters

Scalar Type of scalar values.

template<typename Scalar>

Scalar LSLOpt::OptimizationParameters< Scalar >::gradient_tolerance

parameter for convergence check; BFGS is converged if ||grad|| <= tolerance * max(1.0, ||x||)

template<typename Scalar>

termination criterion for minimal change of function value; BFGS is terminated if (f_{i-1} - f_{i}) / (0.5 * (|f_{i-1}| + |f_{i}|)) <= min_change

template<typename Scalar>

Scalar LSLOpt::OptimizationParameters< Scalar >::min_grad_param

termination criterion of minimal of gradient or parameters; BFGS is terminated if ||s|| or ||r|| are smaller than this value.

The documentation for this struct was generated from the following file: