Nonlinear optimization with box constraints (BOBYQA)

Thread-safe C++ port of minqa::bobyqa(): minimizes a function of many variables subject to box constraints by a trust region method that forms quadratic models by interpolation, using M. J. D. Powell's BOBYQA algorithm. Arguments, defaults, and return value are those of minqa::bobyqa(); see its documentation for details.

Usage

bobyqa(par, fn, lower = -Inf, upper = Inf, control = list(), ...)

Source

M. J. D. Powell's original Fortran 77 BOBYQA code, archived at https://github.com/libprima/prima/tree/main/fortran/original/bobyqa; R interface following the minqa package.

Arguments

par

numeric vector of starting parameters.

fn

function to be minimized; its first argument must be the parameter vector and it must return a scalar numeric value.

lower, upper

numeric vectors of lower and upper bounds (recycled when of length 1).

control

a list of control settings: npt, rhobeg, rhoend, iprint, maxfun, obstop and force.start, as in minqa::bobyqa().

...

further arguments passed to fn.

Value

A list of class c("bobyqa", "minqa") with components par, fval, feval, ierr and msg.

References

M. J. D. Powell (2009), "The BOBYQA algorithm for bound constrained optimization without derivatives", Report No. DAMTP 2009/NA06, Centre for Mathematical Sciences, University of Cambridge.

See also

[newuoa()], and [minqa_c_api] for calling the solvers from parallel C/C++ code.

Examples

fr <- function(x) 100 * (x[2] - x[1]^2)^2 + (1 - x[1])^2
bobyqa(c(1, 2), fr, lower = c(0, 0), upper = c(4, 4))
#> parameter estimates: 0.999999968901681, 0.999999928305543 
#> objective: 9.98796325533312e-15 
#> number of function evaluations: 341