Find optimal two-stage design by constraint minimization

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.

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
if (FALSE) {
minimize(

   ess,

   subject_to(
      toer <= 0.025,
      pow  >= 0.9
   ),

   initial_design = TwoStageDesign(50, .0, 2.0, 60.0, 2.0, 5L)

)
}