Control parameters for the blvim gradient algorithms

This function returns a list of parameters used to tune the gradient algorithms of blvim(). Most of these parameters control the line search algorithm, which is a standard backtracking method with the Armijo stopping criterion. The preconditioner parameter changes the geometry used for the gradient steps.

Usage

blvim_gradient_control(
  rho_init = 0.5,
  shrink = 0.5,
  sufficient_increase = 1e-05,
  ls_iter_max = 50,
  preconditioner = NULL,
  history = FALSE
)

Arguments

rho_init

Initial value of the gradient step in the line search. The step is applied to the rescaled attractivenesses \(U_j\), which sum to one, and has the same meaning for the "gradient" and "gradient_unit" algorithms; see blvim().

shrink

Shrink factor for the gradient step in the line search.

sufficient_increase

Relative sufficient increase in the line search.

ls_iter_max

Maximum number of iterations of the line search.

preconditioner

NULL (default) or a vector of strictly positive values with one value per destination location. The gradient of the potential with respect to the variables of the algorithm (the attractivenesses \(Z_j\) for "gradient" and the rescaled attractivenesses \(U_j\) for "gradient_unit") is multiplied component-wise by this vector, and trial points are projected onto the simplex using the corresponding weighted Euclidean norm. The resulting preconditioner is rescaled to a unit mean in the \(U_j\) variables, so that rho_init keeps its meaning. Only the relative values of the preconditioner matter. The preconditioner does not change the solutions of the problem, but it changes the path followed by the algorithm, and therefore possibly the local maximum it converges to.

history

A logical scalar. If TRUE, the gradient algorithms record the history of their iterations, which can be retrieved with sim_history(). When multiple starting points are used in blvim(), the history is kept only for the retained models (the selected one, or all of them when keep_runs = TRUE).

Value

a list containing the values of the parameters, to be used as the control argument of blvim() or grid_blvim()

References

Armijo, Larry (1966), "Minimization of functions having Lipschitz continuous first partial derivatives", Pacific J. Math. 16 (1): 1–3 doi:10.2140/pjm.1966.16.1

See also

blvim(), grid_blvim(), sim_history()

Examples

blvim_gradient_control(0.5, 0.7, 1e-4, 25)
#> $rho_init
#> [1] 0.5
#> 
#> $shrink
#> [1] 0.7
#> 
#> $sufficient_increase
#> [1] 1e-04
#> 
#> $ls_iter_max
#> [1] 25
#> 
#> $preconditioner
#> NULL
#> 
#> $history
#> [1] FALSE
#> 
## favour moves of the first destination
blvim_gradient_control(preconditioner = c(10, rep(1, 9)))
#> $rho_init
#> [1] 0.5
#> 
#> $shrink
#> [1] 0.5
#> 
#> $sufficient_increase
#> [1] 1e-05
#> 
#> $ls_iter_max
#> [1] 50
#> 
#> $preconditioner
#>  [1] 10  1  1  1  1  1  1  1  1  1
#> 
#> $history
#> [1] FALSE
#>