bobyqa: Bound Optimization by Quadratic Approximation

In nloptr: R Interface to NLopt

Bound Optimization by Quadratic Approximation

Description

BOBYQA performs derivative-free bound-constrained optimization using an iteratively constructed quadratic approximation for the objective function.

Usage

bobyqa(
  x0,
  fn,
  lower = NULL,
  upper = NULL,
  nl.info = FALSE,
  control = list(),
  ...
)

Arguments

x0	starting point for searching the optimum.
fn	objective function that is to be minimized.
lower, upper	lower and upper bound constraints.
nl.info	logical; shall the original NLopt info be shown.
control	list of options, see nl.opts for help.
...	additional arguments passed to the function.

Details

This is an algorithm derived from the BOBYQA Fortran subroutine of Powell, converted to C and modified for the NLopt stopping criteria.

Value

List with components:

par	the optimal solution found so far.
value	the function value corresponding to par.
iter	number of (outer) iterations, see maxeval.
convergence	integer code indicating successful completion (> 0) or a possible error number (< 0).
message	character string produced by NLopt and giving additional information.

Note

Because BOBYQA constructs a quadratic approximation of the objective, it may perform poorly for objective functions that are not twice-differentiable.

References

M. J. D. Powell. “The BOBYQA algorithm for bound constrained optimization without derivatives,” Department of Applied Mathematics and Theoretical Physics, Cambridge England, technical reportNA2009/06 (2009).

See Also

cobyla, newuoa

Examples

## Rosenbrock Banana function

rbf <- function(x) {(1 - x[1]) ^ 2 + 100 * (x[2] - x[1] ^ 2) ^ 2}

## The function as written above has a minimum of 0 at (1, 1)

S <- bobyqa(c(0, 0), rbf)


S

## Rosenbrock Banana function with both parameters constrained to [0, 0.5]

S <- bobyqa(c(0, 0), rbf, lower = c(0, 0), upper = c(0.5, 0.5))

S

nloptr documentation built on July 4, 2024, 1:08 a.m.