minimize takes an unconditional score and
a constraint set (or no constraint) and solves the corresponding
minimization problem using
nloptr
(using COBYLA by default).
An initial design has to be defined. It is also possible to define
lower- and upper-boundary designs. If this is not done, the boundaries are
determined automatically heuristically.
Usage
minimize(
objective,
subject_to,
initial_design,
lower_boundary_design = get_lower_boundary_design(initial_design),
upper_boundary_design = get_upper_boundary_design(initial_design),
opts = list(algorithm = "NLOPT_LN_COBYLA", xtol_rel = 1e-05, maxeval = 10000),
...
)Arguments
- objective
objective function
- subject_to
constraint collection
- initial_design
initial guess (x0 for nloptr)
- lower_boundary_design
design specifying the lower boundary.
- upper_boundary_design
design specifying the upper boundary
- opts
options list passed to nloptr
- ...
further optional arguments passed to
nloptr
Value
a list with elements:
- design
The resulting optimal design
- nloptr_return
Output of the corresponding nloptr call
- call_args
The arguments given to the optimization call
Examples
# Define Type one error rate
toer <- Power(Normal(), PointMassPrior(0.0, 1))
# Define Power at delta = 0.4
pow <- Power(Normal(), PointMassPrior(0.4, 1))
# Define expected sample size at delta = 0.4
ess <- ExpectedSampleSize(Normal(), PointMassPrior(0.4, 1))
# Compute design minimizing ess subject to power and toer constraints
# \donttest{
minimize(
ess,
subject_to(
toer <= 0.025,
pow >= 0.9
),
initial_design = TwoStageDesign(50, .0, 2.0, 60.0, 2.0, 5L)
)
#> $design
#> TwoStageDesign<n1=68;0.3<=x1<=2.3:n2=26-131>
#>
#> $nloptr_return
#>
#> Call:
#> nloptr::nloptr(x0 = tunable_parameters(initial_design), eval_f = f_obj,
#> lb = tunable_parameters(lower_boundary_design), ub = tunable_parameters(upper_boundary_design),
#> eval_g_ineq = g_cnstr, opts = opts)
#>
#>
#> Minimization using NLopt version 2.7.1
#>
#> NLopt solver status: 4 ( NLOPT_XTOL_REACHED: Optimization stopped because
#> xtol_rel or xtol_abs (above) was reached. )
#>
#> Number of Iterations....: 3990
#> Termination conditions: xtol_rel: 1e-05 maxeval: 10000
#> Number of inequality constraints: 3
#> Number of equality constraints: 0
#> Optimal value of objective function: 99.2099508305843
#> Optimal value of controls: 67.77852 0.2812201 2.26569 126.9927 111.6292 86.5138 57.48934 32.48944 2.668702
#> 2.35649 1.822003 1.113608 0.3340881
#>
#>
#>
#> $call_args
#> $call_args$objective
#> E[n(x1)]
#>
#> $call_args$subject_to
#> An object of class "ConstraintsCollection"
#> Slot "unconditional_constraints":
#> [[1]]
#> Pr[x2>=c2(x1)] <= 0.025
#>
#> [[2]]
#> -Pr[x2>=c2(x1)] <= -0.9
#>
#>
#> Slot "conditional_constraints":
#> list()
#>
#>
#> $call_args$initial_design
#> TwoStageDesign<n1=50;0.0<=x1<=2.0:n2=60>
#>
#> $call_args$lower_boundary_design
#> TwoStageDesign<n1=1;-2.0<=x1<=0.0:n2=1>
#>
#> $call_args$upper_boundary_design
#> TwoStageDesign<n1=250;2.0<=x1<=4.0:n2=300>
#>
#> $call_args$opts
#> $call_args$opts$algorithm
#> [1] "NLOPT_LN_COBYLA"
#>
#> $call_args$opts$xtol_rel
#> [1] 1e-05
#>
#> $call_args$opts$maxeval
#> [1] 10000
#>
#>
#>
#> attr(,"class")
#> [1] "adoptrOptimizationResult" "list"
# }